جستجوی مقالات مرتبط با کلیدواژه « Boundary value problems » در نشریات گروه « ریاضی »
تکرار جستجوی کلیدواژه « Boundary value problems » در نشریات گروه « علوم پایه »-
Iranian Journal of Numerical Analysis and Optimization, Volume:13 Issue: 4, Autumn 2023, PP 578 -603In this paper, a high order accuracy method is developed for finding the approximate solution of two-point boundary value problems. The present approach is based on a special algorithm, taken from Pascal’s triangle, for obtaining a generalized form of the parametric splines of degree (2k + 1), k = 1, 2, . . . , which has a lower computational cost and gives the better ap-proximation. Some appropriate band matrices are used to obtain a matrix form for this algorithm.The approximate solution converges to the exact solution of order O(h4k ), where k is a quantity related to the degree of parametric splines and the number of matrix bands that are applied in this paper. Some examples are given to illustrate the applicability of the method, and we compare the computed results with other existing known methods. It isobserved that our approach produced better results.Keywords: Boundary value problems, Parametric spline, Band matrices, Pascal’s triangle}
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International Journal Of Nonlinear Analysis And Applications, Volume:14 Issue: 7, Jul 2023, PP 255 -260In this paper, we convert the fourth-order differential equations with two-point boundary conditions into a differential equation with homogeneous boundary conditions. Because the decomposition methods are closely related to the McLaren series, the McLaren series has a higher accuracy for points close to zero. Then we use Adomian decomposition and homotopy perturbation methods to solve three linear and nonlinear experiments.Keywords: Boundary value problems, Homotopy perturbation method, Adomian Decomposition Method, Modification, stability}
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In this paper, we solve a linear system of second-order boundary value problems by usingthe quadratic B-spline finite element method (FEM). The performance of the method is tested on one model problem. Comparisons are made with both the analytical solution and some recent results.The obtained numerical results show that the method is efficient.Keywords: Finite element method, Quadratic B-splines, Boundary Value Problems}
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In this paper, a new algorithm based on non-polynomial spline is developed for the solution of higher order boundary value problems(BVPs). Employment of the method is done by decomposing the higher order BVP into a system of third order BVPs. Convergence analysis of the developed method is also discussed. The method is tested on higher order linear as well as non-linear BVPs which shows the accuracy and efficiency of the method and also compared our results with some existing fourth order methods.Keywords: Non-polynomial spline, Higher-order, Non-linear, Convergence analysis, Boundary value problems}
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This paper is devoted to the construction of certain polynomials related to Lucas polynomials, namely, modified Lucas polynomials. The constructed modified Lucas polynomials are utilized as basis functions for the numerical treatment of the linear and non-linear second-order boundary value problems (BVPs) involving some specific important problems such as singular and Bratu-type equations. To derive our proposed algorithms, the operational matrix of derivatives of the modified Lucas polynomials is established by expressing the first-order derivative of these polynomials in terms of their original ones. The convergence analysis of the modified Lucas polynomials is deeply discussed by establishing some inequalities concerned with these modified polynomials. Some numerical experiments accompanied by comparisons with some other articles in the literature are presented to demonstrate the applicability and accuracy of the presented algorithms.Keywords: Lucas polynomials, Boundary value problems, Bratu equations, Singular initial value problems, Spectral methods, Operational matrix, Convergence analysis}
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First-kind Chebyshev polynomials are used as the basis functions in this study to present the approximations to the eighth-order boundary-value problems. The problem is reduced using the suggested approach into a set of linear algebraic equations, which are then solved to determine the unknown constants. To demonstrate the application and effectiveness of the strategy, analytical results are provided using tables and graphs for three examples. The results obtained using the proposed method reveal that it is simple and outperforms comparable solutions in the literature.Keywords: First kind Chebyshev polynomials, Boundary value problems, collocation, Approximate Solution}
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The variational iteration algorithm using shifted Chebyshev polynomials of the third kind was used to obtain the numerical solution of seventh order Boundary Value Problems(PVBs) in this paper. The proposed method is made by constructing the shifted Chebyshev polynomials of the third kind for the given boundary value problems and used as a basis functions for the approximation. Numerical examples where also given to show the efficiency and reliability of the proposed method. Calculations were performed using maple 18 software.Keywords: Variational iteration algorithm, Boundary value problems, Shifted Chebyshev polynomials of the third kind, Approximate solutions}
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Iranian Journal of Numerical Analysis and Optimization, Volume:12 Issue: 2, Summer and Autumn 2022, PP 629 -657The complexity of solving differential equations in real-world applications motivates researchers to extend numerical methods. Among different numerical and semi-analytical methods for solving initial and boundary value problems, the differential transform method (DTM) has received no-table attention. It has developed and experienced generalizations for implementing other types of mathematical problems such as optimal control, calculus of variations, and integral equations. This review aims to provide insight into DTM. History, theoretical base, applications, computational aspects, and its revisions are reviewed. The present study helps to understand the theory, capabilities, and features of the DTM, as well as its drawbacks and limitations.Keywords: Boundary value problems, Initial value problems, Differential Transform Method, Semi-analytical methods}
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In the present study, numerical simulations of two-dimensional steady-state incompressible Newtonian fluid flow in one-sided square and two-sided deep lid driven cavities under the aspect ratio K = 1, 4, 6 are reported. For the one-sided lid driven cavity, the upper wall is moved to the right with up to 5000 Reynolds numbers under a grid size of up to 501×501. This lends support to previous findings in the literature with Ghia et al.s results. Three cases are used in this article for the two-sided deep lid driven square cavity specifically. In these cases, the top and lower walls are moved to the right, while the left and right walls remain fixed up to at high Reynolds numbers (5000) under the grid size of up to 201×201. All possible flow solutions are studied in the present article, and flow bifurcation diagrams are constructed as velocity profiles and streamline contours for the same Reynolds number using a finite volume SIMPLE technique. The work done in this paper includes flow properties such as the location of primary and secondary vortices, velocity components, and numerical values for benchmarking purposes, and it is in excellent agreement with previous findings in the literature. A PARAM Shavak, high-performance computing (HPC) computer, was used to execute the calculations.Keywords: partial differential equations, Navier-Stokes equations, Incompressible flow, Lid-driven cavity, Finite volume technique, Boundary value problems}
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In this paper, the existence and the Ulam-Hyers stability of solutions for the implicit second-order differential equations are investigated via fractional-orders integral boundary conditions by direct application of the Banach contraction principle. Finally, we present some particular cases and two examples to illustrate our results.Keywords: Caputo fractional derivative, second-order fractional-order differential equation, Green's function, boundary value problems, nonlocal boundary conditions}
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Journal of Mathematical Analysis and its Contemporary Applications, Volume:3 Issue: 4, Autumn 2021, PP 41 -62This paper investigates the existence of single and multiple positive positive solutions of fractional differential equations with p-Laplacian by means of the Green's function properties, the Guo-Krasnosel'skii fixed point theorem, the monotone iterative technique accompanied by established sufficient conditions and the Leggett-Williams fixed point theorem. Additionally, the main results are illustrated by some examples to show their validity.Keywords: Riemann-Liouville fractional derivative, p-Laplacian operator, Fixed point theorems, Boundary value problems}
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International Journal Of Nonlinear Analysis And Applications, Volume:12 Issue: 1, Winter-Spring 2021, PP 337 -349
We investigate the existence and uniqueness of solutions for multi-point nonlocal boundary value problems of higher-order nonlinear fractional differential equations by using some well known fixed point theorems.
Keywords: boundary value problems, fractional derivative, fixed point theorems} -
In this paper, we apply new type monotone iterative technique which is very rarely used to find iterative solutions for boundary value problem (BVPs) of nonlinear fractional order differential equations (NFODEs). With the help of the aforesaid technique, we establish two sequences of upper and lower solutions for the considered BVP. Further the procedure is testified by providing suitable examples.Keywords: Arbitrary order derivative, Monotone iterative technique, Boundary value problems}
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در سال های اخیر، خین شینگ دو برخی نتایج را روی دسته ای از عملگرهای یکنوای مرکب اثبات کرد. در ادامه همان مقاله، وجود و یگانگی جواب های مثبت را برای معادلات دیفرانسیل کسری غیرخطی به همراه شرایط مرزی داده شده مطالعه و بررسی می کنیم. .
کلید واژگان: مسائل مقدار مرزی, معادلات دیفرانسیل مرتبه کسری, مشتق کسری ریمان- لیوویل, قضیه نقطه ثابت}IntroductionIn this paper, by mixed monotone operators and their fixed points, we investigate the existence and uniqueness of positive solution for the following boundary value problems via nonlinear fractional differential equations.andwhere is the Riemann–Liouville derivative. In recent years, fractional differential equations have been studied by many mathematicians both theoretically and practically, for example, in physics, mechanic, chemistry, engineering, biology, economy, control theory, signal and image processing, biophysics, blood flow phenomena, aerodynamics and etc.First time, mixed monotone operators have been introduced by Guo and Lakshmikantham in 1987. Next, many authors studied them in Banach spaces and obtained some results not only in theory fields but also wide applications in chemistry, engineering, biology, technology and other fields. In 2009, Xu et. al studied the properties of Greenchr('39')s function for the nonlinear fractional differential equation boundary value problem (2). Here, the existence and uniqueness of its positive solutions are obtained by using the properties of cone and fixed point theorems for mixed monotone operators. As an application, we utilize the obtained results to study the existence and uniqueness of positive solution for nonlinear fractional differential equation boundary value problems.
Material and methodsThe content of this paper is organized as follows. First, we present some definitions, lemmas and basic results that will be used in the proofs of our theorems. Then, we consider the existence and uniqueness of positive solution for the operator equation, also we utilize the results obtained to study the existence and uniqueness of positive solution for nonlinear fractional differential equation boundary value problems.
Results and discussionIn this work, we study the existence and uniqueness of positive solutions for nonlinear fractional differential equation boundary-value problems. Our results guarantee the existence of a unique positive solution, and can be applied for constructing an iterative scheme for obtaining the solution.
ConclusionThe following conclusions were drawn from this research.
Using the properties of cones and the fixed point theorem for mixed monotone operator, the existence and uniqueness of the positive solution are obtained. Our research methods are different from those in the related literature. As an application, we utilize the obtained results to study the existence and uniqueness of positive solution for nonlinear fractional differential equation boundary value problems. Our results extend and improve the related conclusions in the literature.* The formula is not displayed correctly.
Keywords: Boundary value problems, Fractional differential equations, Mixed monotone operator, Fixed point theorem.o} -
In this study, improved Sinc-Galerkin and Sinc-collocation methods are developed based on double exponential transformation to solve a one-dimensional Bratu-type equation. The properties of these methods are used to reduce the solution of the nonlinear problem to the solution of nonlinear algebraic equations. For simplicity in solving the nonlinear system, a matrix vector form of the nonlinear system is found. The upper bound of the error for the Sinc-Galerkin is determined. Also the numerical approximations are compared with the best results reported in the literature. The results confirm that both the Sinc-Galerkin and the Sinc-collocation methods have the same accuracy, but they are significantly more accurate than the other existing methods.Keywords: Sinc-Galerkin, Sinc-collocation, Bratu's problem, double exponential transformation, boundary value problems}
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در این مقاله با استفاده از قضیه هایی که توسط پروفسور ریچری در مقاله [8] و پروفسور بوناننو در مقاله [6] اثبات شده است، وجود حداقل سه جواب ضعیف را برای یک دستگاه شبه خطی بیضوی ثابت خواهیم کرد. در واقع، ما به دستگاه معادله دیفرانسیل یک عملگر غیرخطی مشتق پذیر نسبت خواهیم داد به طوری که نقاط بحرانی این عملگر جواب های ضعیف از دستگاه مورد نظر باشند.
کلید واژگان: مسائل مقدارمرزی, روش تغییراتی, سه جواب ضعیف}In this paper, applying two theorems of Ricceri and Bonanno, we will establish the existence of three weak solutions for a quasilinear elliptic system. Indeed, we will assign a differentiable nonlinear operator to a differential equation system such that the critical points of this operator are weak solutions of the system. In this paper, applying two theorems of Ricceri and Bonanno, we will establish the existence of three weak solutions for a quasilinear elliptic system. Indeed, we will assign a differentiable nonlinear operator to a differential equation system such that the critical points of this operator are weak solutions of the system. In this paper, applying two theorems of Ricceri and Bonanno, we will establish the existence of three weak solutions for a quasilinear elliptic system. Indeed, we will assign a differentiable nonlinear operator to a differential equation system such that the critical points of this operator are weak solutions of the system.
Keywords: Boundary value problems, variational method, three weak solutions} -
In this paper, the issue of distribution of zeros of the solutions of linear homogenous differential equations (LHDE) have been investigated in terms of semi-critical intervals. We shall follow a geometric approach to state and prove some properties of LHDEs of the sixth order with (2, 3, 4, and 5 points) boundary conditions and with measurable coefficients. Moreover, the relations between semi-critical intervals of the LHDEs have been explored. Also, the obtained results have been generalized for the 5th order differential equations.
Keywords: Linear differential equations, Distribution of zeros for the solution, Boundary value problems, Semi-oscillatory interval, Semi-critical interval} -
In this article, Modified Hermite wavelets based numerical method is developed for the solution of singular initial and boundary value problems. It consists of reducing the differential equations with the associated initial and boundary conditions into system of algebraic equations by expanding the unknown function as a series of Hermite wavelets with unknown coefficients. Obtained system of equations are solved using Newton’s iterative method through Matlab. Illustrative examples are considered to demonstrate the applicability and accuracy of the proposed technique. Obtained results are compared favorably with the exact solutions. Also, we proved the theorem reveals that, when exact solution can be obtained by the proposed method.Keywords: Hermite wavelets, Singular initial, boundary value problems, Collocation method, Limit points}
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International Journal Of Nonlinear Analysis And Applications, Volume:9 Issue: 1, Summer - Autumn 2018, PP 247 -260In this paper, we concerned with positive solutions for higher order m-point nonlinear fractional boundary value problems with integral boundary conditions. We establish the criteria for the existence of at least one, two and three positive solutions for higher order m-point nonlinear fractional boundary value problems with integral boundary conditions by using a result from the theory of fixed point index, Avery-Henderson fixed point theorem and the Legget-Williams fixed point theorem, respectively.Keywords: Boundary value problems, cone, fixed point theorems, positive solutions, Riemann-Liouville fractional derivative, integral boundary conditions}
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در این مقاله، نویسندگان یک الگوریتم تحلیلی همگرای اصلاح شده را برای جواب مسائل مقدار مرزی و مقدار اولیه غیرخطی به واسطه روش تغییر پارامتر ارائه می کنند و بطور خلاصه روش تغییر پارامتر بهینه می نامند. این روش براساس تعبیه یک پارامتر و یک عملگر کمکی، یک مزیت محاسباتی برای همگرایی جواب های تقریبی معادلات دیفرانسیل غیرخطی مهیا می کند. همگرایی توسعه یافته مذ کور نشان داده شده و جزییات آن نیز مورد بحث قرار می گیرد.
علاوه بر این، یک روش مناسب برای انتخاب مقدار بهینه پارامتر کمکی در نظر گرفته می شود که تحت مینیمم سازی خطا روی دامنه مساله می باشد. موثر بودن روش و دقت الگوریتم پیشنهادی، با اجرا روی مسائل فیزیکی همچون مساله استورم- لیوویل، مساله ایری و مساله نوسانگر هارمونیک کوانتومی نشان داده می شود. نتایج عددی و شکل های بدست آمده بوضوح دقت الگوریتم و همگرایی آن را منعکس می کند.کلید واژگان: روش تغییر پارامتر بهینه, مسائل مقدار مرزی, مساله استورم, لیوویل, مساله ایری و مساله نوسانگر هارمونیک مکانیکی کوانتومی}In this paper, the authors present a modified convergent analytic algorithm for the solution of nonlinear boundary value problems by means of a variable parameter method and briefly, the method is called optimal variable parameter method. This method, based on the embedding of a parameter and an auxiliary operator, provides a computational advantage for the convergence of the approximate solutions of nonlinear differential equations. The developed convergence has been shown and its details are discussed. Additionally, a convenient method is considered for selecting an optimal value of the auxiliary parameter, via minimizing the residual error over the domain of problem.
The effectiveness of the method and the accuracy of the proposed algorithm are illustrated by the implementation of physical problems such as Sturm-Liouville problem, Airy equation, and Quantum mechanical harmonic oscillator problem.
The numerical results and obtained demonstrate clearly reflect the accuracy of the method and its convergence.Keywords: Optimal variation of parameter method (OVPM), Boundary value problems, Sturm- Liouville, Airy, Quantum mechanical harmonic oscillator problems}
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