جستجوی مقالات مرتبط با کلیدواژه « Convergence » در نشریات گروه « ریاضی »
تکرار جستجوی کلیدواژه «Convergence» در نشریات گروه «علوم پایه»-
International Journal Of Nonlinear Analysis And Applications, Volume:15 Issue: 12, Dec 2024, PP 453 -464In this paper, we defined $\alpha_{G}-$admissible interpolative type contraction mappings in $G$-metric spaces. We proved some convergence results for such classes of mappings using the properties of $G$-metric space and found the fixed point results for such contractive mappings. To elaborate on the results we provided some examples, which show that our results hold in the setting of $G-$metric spaces.Keywords: G-Metric Space, Convergence, Interpolation, Fixed Point}
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In the proposed manuscript, the solution of the fuzzy nonlinear optimization problems (FNLOPs) is gainedusing a projection recurrent neural network (RNN) scheme. Since there is a few research for resolving of FNLOPby RNN's, we establish a new scheme to solve the problem. By reducing theoriginal program to an interval problem and then weighting problem, the Karush--Kuhn--Tucker (KKT)conditions are presented. Moreover, we apply the KKT conditions into a RNN as a efficient tool to solve the problem. Besides, the convergence properties and thestability analysis of the system model are provided. In the final step, several simulation examples are verified to support the obtained results. Reported results are compared with some other previous neural networks.Keywords: Neural Networks, Fuzzy Nonlinear Programming Problem, Fuzzy Parameters, Stability, Convergence}
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The objective of this paper is to present a finite difference scheme that estimates the solution of space fractional diffusion equation with the Caputo fractional derivative. The proposed scheme’s stability, and convergence are proved. To assess the efficiency of this program, a set of tests is carried out. The results of these tests demonstrate the reliability and accuracy of the proposed scheme.
Keywords: Space Fractional Diffusion Equation, Convergence, Stability, Finite Difference Method} -
We present a numerical method for solving Fredholm twodimensional integral equations in this study. Our approach is based on two-dimensional Lagrange interpolation polynomials. The use of interpolation is that instead of the unknown function, we use the Lagrange interpolator polynomial, and then by solving these linear equation system, we obtain the Lagrange coefficients, which are the second components of the support points, approximately. By putting these coefficients in the Lagrange finder function, we get an approximation to the exact answer. A numerical algorithm is described for this purpose, and two cases are solved using this algorithm. Furthermore, a theorem is proved to demonstrate the algorithm’s convergence and to obtain an upper bound on the distance between the exact and numerical solutions.
Keywords: Two-Dimensional Integral Equation, Fredholm Integral Equation, Lagrange Interpolation, Convergence} -
The aim of this manuscript is to introduce and analyze a stochastic finite difference scheme for Ito stochastic partial differential equations. We also discuss the consistency, stability, and convergence for the stochastic finite difference scheme. The numerical simulations obtained from the proposed stochastic finite difference scheme show the efficiency of the suggested stochastic finite difference scheme.
Keywords: Stochastic partial differential equations, Stochastic finite difference scheme, Stability, Consistency, Convergence} -
در این مقاله روش هم محلی را برای حل عددی معادلات انتگرال دوبعدی ولترا تعمیم می دهیم. برای این منظور ابتدا وجود و یکتایی جواب این نوع معادلات را ثابت کرده و یک نمایش هسته حلال برای جواب آنها ارایه می کنیم. سپس روش هم محلی با استفاده از چند جمله ای های قطعه ای را برای حل معادلات مذکور تعمیم داده و دستگاه معادلات جبری متناظر را به دست آورده و نشان می دهیم دستگاه مذکور دارای جواب یکتاست. هم چنین همگرایی روش را ثابت کرده و مرتبه ی همگرایی روش را با اثبات قضیه ای به دست می آوریم. سرانجام چند مثال عددی برای نشان دادن کارایی روش و تایید نتایج نظری به دست آمده، ارایه می کنیم.
کلید واژگان: معادله انتگرال دوبعدی ولترا, روش هم محلی, چندجمله ای های قطعه ای, همگرایی}In this paper, we extend the collocation method for the numerical solution of two-dimensional Volterra integral equations. For this purpose, we first prove the existence and uniqueness of the solution of these types of equations and present a resolvent kernel representation for their solution. Then, we extend the collocation method using piecewise polynomials to solve the mentioned equations and obtain the corresponding algebraic system of equations and show that the system has a unique solution. We also prove the convergence of the method and obtain the order of convergence of the method by proving a theorem. Finally, we present some numerical examples to show the efficiency of the method and confirm the obtained theoretical results.
Keywords: Two-dimensional Volterra integral equations, Collocation method, Piecewise polynomials, convergence} -
In this paper, we present a well-organized strategy to estimate the fractional advection-diffusion equations, which is an important class of equations that arises in many application fields. Thus, Lagrange square interpolation is applied in the discretization of the fractional temporal derivative, and the weighted and shifted Legendre polynomials as operators are exploited to discretize the spatial fractional derivatives of the space-fractional term in multi-termtime fractional advection-diffusion model. The privilege of the numerical method is the orthogonality of Legendre polynomials and its operational matrices which reduces time computation and increases speed. A second-order implicit technique is given, and its stability and convergence are investigated. Finally, we propose three numerical examples to check the validity and numerical results to illustrate the precision and efficiency of the new approach.Keywords: Advection-diffusion model, multi-term time fractional term, collocation method, Legendre polynomial, Stability, Convergence}
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Iranian Journal of Numerical Analysis and Optimization, Volume:13 Issue: 4, Autumn 2023, PP 711 -727The present study addresses an exponentially fitted finite difference method to obtain the solution of singularly perturbed two-point boundary value problems (BVPs) having a boundary layer at one end (left or right) point on uniform mesh. A fitting factor is introduced in the derived scheme using the theory of singular perturbations. Thomas algorithm is employed to solve the resulting tri-diagonal system of equations. The convergence of the presented method is investigated. Several model example problems are solved using the proposed method. The results are presented with terms of maximum absolute errors, which demonstrate the accuracy and efficiency of the method. It is observed that the proposed method is capable of producing highly accurate results with minimal computational effort for a fixed value of step size h, when the perturbation parameter tends to zero. From the graphs, we also observed that a numerical solution approximates the exact solution very well in the boundary layers for smaller value of ε.Keywords: Singular perturbation problem, Stability, convergence, finite difference method}
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ریسک عملیاتی یکی از ریسک های شناسایی شده در سازمان ها بالاخص در بانک ها است و کمیته های نظارت بانکی توجه ویژه ای به آن دارند. در این مقاله مدل ریاضی بر اساس مدل پیشرفته ریسک عملیاتی برای محاسبه احتمال بقای بانک به صورت یک معادله انتگرال دیفرانسیل جزیی ولترا در نظر گرفته شده است. این معادله با به کارگیری روش تفاضلات متناهی با قاعده ذوزنقه ای جهت تخمین بخش انتگرالی آن به صورت عددی حل و تاثیر تغییر پارامترهای مدل بر خروجی مساله بررسی شده است. علاوه بر این، پایداری و همگرایی روش، مورد بحث قرار گرفته و نتایج عددی آن ارایه شده است.
کلید واژگان: ریسک عملیاتی, معادله انتگرال-دیفرانسیل جزیی, تفاضلات متناهی, پایداری, همگرایی}Operational risk is one of the identified risks in organizations, especially in banks, and Basel committees on banking supervision pay special attention to it. In this paper, the mathematical model based on the advanced operational risk model is considered to calculate the probability of survive as a partial Volterra integro-differentail equation. This equation has been solved numerically by applying the finite differences method with trapezoidal rule to estimate its integral part and the effect of changing the model parameters on the output of the problem has been investigated. In addition, the stability and convergence of the method are discussed and its numerical results are presented.
Keywords: Operational risk, partial integro-differential equation, finite differences, Stability, Convergence} -
International Journal Of Nonlinear Analysis And Applications, Volume:14 Issue: 6, Jun 2023, PP 371 -386In this paper, we introduce a new iteration process for the approximation of fixed points. We show that our iteration process is faster than the existing iteration processes like the M-iteration process and the K-iteration process for contraction mappings. Also, we prove that the new iteration process is stable. Finally, we study the convergence of a new iterative scheme to a fixed point for the $(\alpha,\beta)$ -Reich-Suzuki nonexpansive type mappings in Banach space.Keywords: Fixed point, convergence, Opial’s condition, generalized nonexpansive mappings}
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In this paper, we prove that a faster iterative algorithm can be used to reach the solution of the Volterra functional integral equation of the second kind. Also, we show that a data dependence result can be obtained for this integral equation and to support this result we give an example.
Keywords: Iterative algorithm, contraction principle, volterra integral equation, convergence, data dependence} -
در این مقاله با استفاده از دو روش پیشنهادی، تقریبی به مراتب کاراتر نسبت به روش های عددی موجود برای دسترسی به جواب های عددی معادله ریکاتی کسری ارایه می گردد. این تقریب برای جواب معادله ریکاتی کسری بر پایه استفاده از توابع اسپلاین نمایی پیشنهاد می شود. سپس روابط سازگار اسپلاین نمایی به دست آمده و معادله دیفرانسیل ریکاتی کسری گسسته سازی می گردد و براثر اجرای این عملیات ریاضی یک دستگاه جبری از معادلات به دست می آید. به جهت بیان مزایای روش های پیشنهادی در این مقاله تحلیل خطا و همگرایی نیز بر اساس این اسپلاین نمایی مورد بحث قرار می گیرد. و نهایتا هر دو روش پیشنهادی از مرتبه همگرایی دو برخوردار می باشند. از اهم مزایای این روش های پیشنهادی این است که این روش ها نه تنها برای حل معادلات ریکاتی کسری، بلکه برای انواع معادلات کسری می تواند مورد استفاده قرار بگیرد. برای نشان دادن کارایی این روش ها، مثال های عددی از نوع معادلات ریکاتی کسری به واسطه این روش ها حل و نتایج به دست آمده را با نتایج سایر روش های عددی موجود مقایسه و این ادعا ثابت می گردد، که روش های موصوف تقریب خوبی برای معادله دیفرانسیل ریکاتی کسری می باشند.
کلید واژگان: معادله دیفرانسیل ریکاتی کسری, مشتق کاپوتو, اسپلاین نمایی, همگرایی}In this Article, proposes an approximation for the solution of the Riccati equation based on the use of exponential spline functions. Then the exponential spline equations are obtained and the differential equation of the fractional Riccati is discretized. The effect of performing this mathematical operation is obtained from an algebraic system of equations. To illustrate the benefits of the method proposed here the error analysis and convergence article are also discussed based on this exponential spline. Finally, a second-order method is obtained. One of the benefits of this proposed method is that it is not only for solving fractional Riccati equations, but also for a variety of Fractional equations that can be used. To illustrate the effectiveness of this method by solving numerical examples and a comparison of the results obtained from the implementation of this proposed method with the results of other existing numerical methods proves the claim that the proposed method is a good approximation for the fractional Riccati equations.
Keywords: Fractional riccati differential equation, Caputo derivative, Exponential Spline, convergence} -
This paper focuses on the numerical solution of the time-fractional telegraph equation in Caputo sense with $1 < beta < 2$. The time-fractional telegraph equation models neutron transport inside the core of a nuclear reactor. The proposed numerical solution consists of two stages. First, the time-discretized scheme of this equation is obtained by the Crank-Nicolson method. The stability and convergence of results from the semi-discretized scheme are presented. In the second stage, the numerical approximation of the unknown function at specific points is achieved through the collocation method using the moving least square method. The numerical experiments analyze the impact of some parameters of the proposed method.Keywords: Time-Fractional Telegraph Equation, Moving least squares method, Stability, Convergence}
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International Journal Of Nonlinear Analysis And Applications, Volume:14 Issue: 2, Feb 2023, PP 45 -74Recently, the authors introduce a four-step iterative algorithm called the UD-iteration scheme (Udofia and Igbokwe [35]). Here we introduce the multivalued version of the UD-iteration scheme and show that it can be used to approximate the fixed points of multivalued contraction and multivalued generalized $\alpha$-nonexpansive mappings. we prove strong and weak convergence of the iteration scheme to the fixed point of multivalued generalized $\alpha$-nonexpansive mapping. We also prove that the scheme is $\varUpsilon$-stable and Data dependent. Convergence analysis shows that the multivalued UD-iteration scheme has a faster rate of convergence for multivalued contraction and multivalued generalized $\alpha$-nonexpansive mappings than some well-known existing iteration schemes in the literature.Keywords: uniformly convex Banach space, Multivalued generalized $, alpha$-nonexpansive Mapping, convergence, data dependence, stability}
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In this work, a non-classical sinc-collocation method is used to find numerical solution of third-order boundary value problems. The novelty of this approach is based on using the weight functions in the traditional sinc- expansion. The properties of sinc-collocation are used to reduce the boundary value problems to a nonlinear system of algebraic equations which can be solved numerically. In addition, the convergence of the proposed method is discussed by preparing the theorems which show exponential convergence and guarantee its applicability. Several examples are solved and the numerical results show the efficiency and applicability of the method.Keywords: Non-classical, Sinc Collocation method, Third-order, Boundary value problem, Convergence}
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International Journal Of Nonlinear Analysis And Applications, Volume:14 Issue: 1, Jan 2023, PP 309 -324In this paper, we consider some new classes of general bivariational inclusions. It is shown that the general bivariational inclusions are equivalent to the fixed point problems, resolvent equations and dynamical systems. We have discussed the existence of a solution of the general bivariational inequalities. Some new iterative methods for solving general bivariational inclusions and related optimization problems are suggested by using resolvent methods, resolvent equations and dynamical systems coupled with finite difference technique. Convergence analysis of these methods is investigated under monotonicity. Some special cases are also discussed as applications of the main results.Keywords: Variational inclusions, Existence results, resolvent method, resolvent equations, Dynamical system, convergence}
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In this paper, a pseudospectral method is proposed for solving the nonlinear time-fractional Klein-Gordon and sine-Gordon equations. The method is based on the Sinc operational matrices. A finite difference scheme is used to discretize the Caputo time-fractional derivative, while the spatial derivatives are approximated by the Sinc method. The convergence of the full discretization of the problem is studied. Some numerical examples are presented to confirm the accuracy and efficiency of the proposed method. The numerical results are compared with the analytical solution and the reported results in the literature.Keywords: fractional differential equation, Nonlinear Klein-Gordon, sine-Gordon equations, Sinc operational matrices, Pseudospectral method, Convergence}
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This study concentrated on the numerical solution of a nonlinear Volterra integral equation. The approach is accorded to a type of orthogonal wavelets named the Chebyshev cardinal wavelets. The undetermined solution is extended concerning the Chebyshev cardinal wavelets involving unknown coefficients. Hence, a system of nonlinear algebraic equations is drawn out by changing the introduced expansion to the predetermined problem, applying the generated operational matrix, and supposing the cardinality of the basis functions. Conclusively, the estimated solution is achieved by figuring out the mentioned system. Relatively, the convergence of the founded procedure process is reviewed in the Sobolev space. In addition, the results achieved from utilizing the method in some instances display the applicability and validity of the method.Keywords: Volterra integral equation, Chebyshev Wavelets, operational matrix, Convergence, Sobolev space}
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The theory of interval-valued difference equations under $gH$-difference is an interesting topic, since it can be applied to study numerical solutions to interval-valued or fuzzy-valued differential equations. In this paper, we estimate the number of solutions to a class of first-order interval-valued difference equations under $gH$-difference, which reveals the complexity of the stability analysis in this area, as well as the difficulty for prediction and control problems. Then, based on the relative positions of initial values and equilibrium points, we provide sufficient conditions for the existence of convergent solutions. We also provide examples to illustrate the validity of our results.Keywords: Interval-valued difference equations, gH-difference, equilibrium points, Convergence}
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در این مقاله، یک اثبات ساختاری برای مطالعه وجود و منحصر به فرد بودن جواب مساله منفرد زیر با شرایط مرزی ارایه می شود. به طور کلی فرض می شود که نسبت متغیر مستقل نامنفرد باشد. اما مجاز است نسبت به منفرد باشد. دنباله تکراری پیکارد را با ساخت معادله انتگرالی که تابع گرین در آن منفی نیست، اعمال می کنیم. سپس همگرایی این دنباله تکراری توسط یک پارامتر نشانده کنترل می شود. سریعترین همگرایی برای یک پارامتر نشانده بهینه رخ می دهد که یک تابع خاص را به حداکثر می رساند. این مسیله بهینه سازی دنباله ای با سرعت بالایی از همگرایی به جواب یکتا به ارمغان می آورد بطوریکه در ناحیه محدود به آن باید مثبت باشد. چند مثال گویا برای تایید اعتبار و پایایی این بحث ساختلری آورده شده است.
کلید واژگان: مساله مقدار مرزی منفرد, قضیه ساختاری, وجود و منحصر به فرد بودن}The convergence of thisiterative sequence is then controlled by an embedded parameter. The fastest convergence occurs for an optimal embedded parameter which maximizes a special function. This optimization problem brings a sequence with high rate of the convergence to theunique solution in the finite region where $\frac{\partial f}{\partial y}$ has to be positive.Some illustrative examples are given to confirm the validity and reliability of this constructive theory.
Keywords: Singular boundary value problem, Constructive theorem, Existence, uniqueness, Convergence}
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