جستجوی مقالات مرتبط با کلیدواژه « differential equation » در نشریات گروه « ریاضی »
تکرار جستجوی کلیدواژه «differential equation» در نشریات گروه «علوم پایه»-
We introduce the Hausdorff measure of noncompactness in the sequence space $bv_{\infty}$ and investigate the existence of solution of infinite systems of differential equations with respect to Hausdorff measure of noncompactness. Finally, we present an example to defend of theorem of existential.Keywords: Green function, Differential equation, measure of noncompactness, Meir-Keeler condensing operator, sequence space}
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In this present study, the tumor growth model using the Gompertz equation with the Allee effect is developed under a fuzzy environment using the Generalized Hukuhara Derivative (GHD) approach. To capture the tumor growth patterns with the Allee threshold, the parameters present in the model vary from time to time, and in real life, it is very difficult to estimate the exact cell count. In this vague situation, the initial condition, coefficient, and both together are taken as the fuzzy number. In this paper, the GHD approach is used to solve the fuzzy tumor growth model in which four different cases are considered with respect to (i)-gH differentiability and (ii)-gH differentiability concept. The main objective of this study is to present a significant reduction in uncertainty while modeling the tumor growth in a fuzzy environment with the Allee effect. Finally, the proposed model and technique are illustrated by numerical simulation and analysis of tumor growth is conducted.Keywords: Mathematical Modeling, gH-Derivative Approach, Fuzzy theory, tumor growth, Allee Effect, differential equation, Soft Computing}
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International Journal Of Nonlinear Analysis And Applications, Volume:14 Issue: 2, Feb 2023, PP 87 -100In this paper, we further develop the notion of cyclic $(\alpha, \beta)$-admissible mappings introduced in (\cite{tac}, S. Chandok, K. Tas, A. H. Ansari, \emph{Some fixed point results for TAC-type contractive mappings,} J. Function spaces, 2016, Article ID 1907676, 1--6) and $(\psi, F)$-contraction mappings introduced in ( \cite{wad1}, D. Wardowski, \emph{Solving existence problems via $F$-contractions,} Proceedings of the American Mathematical Society, 146 (4), (2018), 1585--1598), in the framework of $b$-metric spaces. To achieve this, we introduce the notion of $(\alpha,\beta)-S$-admissible mappings and a new class of generalized $(\psi, F)$-contraction types and establish a common fixed point and fixed point results for these classes of mappings in the framework of complete $b$-metric spaces. As an application, we establish the existence and uniqueness of the solutions to differential equations in the framework of fractional derivatives involving Mittag-Leffler kernels via the fixed point technique. The results obtained in this work provide extension as well as substantial generalization and improvement of the fixed point results obtained in \cite{tac,wad1, wad} and several well-known results on fixed point theory and its applications.Keywords: Fixed point, $(alpha, beta)-S$-admissible mappings, Generalized $(, psi, F)$-contraction, $b$-metric space, Differential equation}
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Mathematical modeling has been a significant tool in biological sciences for several decades. Modern agricultural practices have had numerous effects on different aspects of ecosystems, particularly on animal populations. This research focuses on road collisions involving wildlife and emphasizes the effects of agricultural and non-agricultural surrounding lands. Using non-parametric Mann-Whitney U and Spearman's Rank tests, as well as SPSS software, the study found that the highest number of wildlife deaths, especially for mammals, birds, and reptiles, occurred in areas surrounded by natural regions (non-agricultural lands). Furthermore, the study found that the number of casualties was highest in the middle month of spring and those morning observations resulted in more collisions than evening ones. The correlation coefficients confirmed a significant relationship between the frequency of accidents and the type of surrounding landscape. Additionally, the researchers proposed a logistic mathematical model to investigate the relationship between animal losses and vehicle collisions. After identifying the equilibrium points, the study analyzed the solution behavior around these points.Keywords: Agricultural Surrounding, Road Mortality, Differential Equation}
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This work deals with the existence of periodic solutions (EPSs) to a third order nonlinear delay differential equation (DDE) with multiple constant delays. For the considered DDE, a theorem is proved, which includes sufficient criteria related to the EPSs. The technique of the proof depends on Lyapunov-Krasovskiˇı functional (LKF) approach. The obtained result extends and improves some results that can be found in the literature. In a particular case of the considered DDE, an example is provided to show the applicability of the main result of this paper.Keywords: existence, periodic solutions, Differential equation, third order, delay, LKF}
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Application of reproducing kernel Hilbert space method for generalized 1-D linear telegraph equationInternational Journal Of Nonlinear Analysis And Applications, Volume:13 Issue: 2, Summer-Autumn 2022, PP 485 -497
This paper presents the generalized 1-D linear telegraph equation. We have solved this equation by the Reproducing Kernel Hilbert Space (RKHS) method and compared it with other methods like fourth-order compact difference and alternating direction implicit schemes and meshless local radial point interpolation (MLRPI). Comparing the results of these three methods as well as comparing the exact solution, indicating the efficiency and validity of RKHS. The uniformly converges of the computed solution to the analytical solution are proved. Note that the procedure is easy to implement, and it no needs discretization, and is mesh-free too.
Keywords: Reproducing Kernel Hilbert Space (RKHS), Telegraph equations, Gram-Schmidt orthogonalization process, Differential equation} -
International Journal Of Nonlinear Analysis And Applications, Volume:13 Issue: 1, Winter-Spring 2022, PP 2897 -2909
In this paper our main goal is to study the climatology and variability of the frequency of thunderstorm days over Bangladesh region throughout the year. It has been found that the mean thunderstorm days increase significantly from March to May, i.e. during the pre-monsoon season, although the graphical devices show that there does not seem to be much deviation from the occurrences of thunderstorms each year. The mean monthly and seasonal thunderstorm days were maximum in 1993, followed by that in 1997; whereas it was a minimum in the year 1980, with an extension in its frequency in the subsequent years 1981 and 1982. The coefficient of variation of both annual and seasonal thunderstorm days is minimum over the areas of maximum frequency of mean thunderstorm days and vice-versa. The time-domain analysis confirms that the occurrence happened to be maximum in the year 1991, although each and every state did not witness thunderstorms every year. Also some other time-domain models like autocorrelation and seasonal integrated moving average provide adequate evidence for exploring the number of thunderstorms which happen to confirm the trend of occurrence of thunderstorm over the years.
Keywords: Thunderstorm, frequency, differential equation, interpolation, extrapolation, autocorrelation function, ARIMA} -
For a given subspace as a solution space of a linear ODE, we define a special linear parametric group action and prolong it to the jet bundle. We determine these group parameters by moving frame method and prove that these group parameters are the first integrals of the given ODE. These first integrals are used to construct the general form of operators which preserve given subspace invariant.Keywords: First integral, moving frame, group action, Differential equation, invariant subspace}
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One of the schemes to find the optimal shape parameter and optimal number of points in the radial basis function (RBF) methods is to apply the stochastic arithmetic (SA) in place of the common floating-point arithmetic (FPA). The main purpose of this work is to introduce a reliable approach based on this new arithmetic to compute the local optimal shape parameter and number of points in multiquadric and Gaussian RBF-meshless methods for solving differential equations, in the iterative process. To this end, the CESTAC method is applied. Also, in order to implement the proposed algorithms, the CADNA library is performed. The examples illustrate the efficiency and importance of using this library to validate the results.
Keywords: Stochastic Arithmetic, CESTAC method, CADNA library, Differential equation, Radial basis function (RBF)} -
Berinde [V. Berinde, Approximating fixed points of weak contractions using the Picard iteration, Nonlinear Anal. Forum {bf 9} (2004), 43-53] introduced almost contraction mappings and proved Banach contraction principle for such mappings. The aim of this paper is to introduce the notion of multivalued almost $Theta$- contraction mappings andto prove some best proximity point results for this new class of mappings. As applications, best proximity point and fixed point results for weak single valued $Theta$-contraction mappings are obtained. Moreover, we give an example to support the results presented herein. An application to a nonlinear differential equation is also provided.Keywords: Almost contraction, $Theta$-contraction, best proximity points, differential equation}
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This paper successfully applies the Adomian decomposition and the modified Laplace Adomian decomposition methods to find the approximate solution of a nonlinear fractional Volterra-Fredholm integro-differential equation. The reliability of the methods and reduction in the size of the computational work give these methods a wider applicability. Also, the behavior of the solution can be formally determined by analytical approximate. Moreover, the paper proves the convergence and uniqueness of the solution. Finally, this study includes an example to demonstrate the validity and applicability of the proposed techniques.Keywords: Laplace transform, Adomian decomposition method, fractional Volterra, Fredholm integro, differential equation, Caputo fractional derivative}
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با هدف یافتن جوابهای عددی برخی از مسائل کلاسیک روشی بر مبنای فازی ارایه می دهیم.
تبدیل را بکار می بریم. - F برای حل یک معادله دیفرانسیل معمولی از مرتبه دو و با شرایط مرزی ، تکنیک ما مسئله را به سیستم معادلات خطی تقلیل می دهیم وسعی می کنیم تا کاربردی بودن روش پیشنهادی را تبدیل نه تنها - F نشان دهیم. دقت روش پیشنهادی را ارزیابی می کنیم و نشان می دهیم که روش براساس مجموعه ی کاربردهایش را توسیع می دهد، بلکه در حل مسائل بدحالت دارای مزایایی می باشد.We propose a fuzzy-based approach aiming at finding numerical solutions to some classical problems. We use the technique of F-transform to solve a second-order ordinary differential equation with boundary conditions. We reduce the problem to a system of linear equations and make experiments that demonstrate applicability of the proposed method. We estimate the order of accuracy of the proposed method. We show that the F-transform-based approach does not only extend the set of its applications, but has a certain advantage in the solution of ill-posed problems.Keywords: F, transform, Differential equation, Boundary value problem, Second order differential equation} -
In this paper, a fuzzy numerical procedure for solving fuzzy linear Volterra integro-differential equations of the second kind under strong generalized differentiability is designed. Unlike the existing numerical methods, we do not replace the original fuzzy equation by a $2\times 2$ system of crisp equations, that is the main difference between our method and other numerical methods. Error analysis and numerical examples are given to show the convergency and efficiency of the proposed method, respectively.Keywords: Fuzzy number, Fuzzy linear Volterra integro, differential equation, Generalized differentiability, Fuzzy trapezoidal rule}
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In this study, we give the relationships between the conical curvatures of ruled surfaces generated by the unit vectors of the ruling, central normal and central tangent of a ruled surface in the Euclidean 3-space E^3. We obtain differential equations characterizing slant ruled surfaces and if the reference ruled surface is a slant ruled surface, we give the conditions for the surfaces generated by central normal and central tangent vectors to be slant ruled surfaces.
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Keywords: Slant ruled surface, Frenet frame, Conical curvature, Differential equation} -
In this paper, we consider a boundary value problem with aftereffect on a finite interval. Then, the asymptotic behavior of the solutions, eigenvalues, the nodal points and the associated nodal length are studied. We also calculate the numerical values of the nodal points and the nodal length. Finally, we prove the uniqueness theorem for the inverse aftereffect problem by applying any dense subset of the nodal points.
Keywords: Differential equation, aftereffect, uniquenesstheorem, nodal points} -
Iranian Journal of Numerical Analysis and Optimization, Volume:5 Issue: 1, Winter and Spring 2015, PP 73 -83We present here the numerical solution of damped forced oscillator problem using Haar wavelet and compare the numerical results obtained with some well-known numerical methods such as Runge-Kutta fourth order classical and Taylor Series methods. Numerical results show that the present Haar wavelet method gives more accurate approximations than above said numerical methods.Keywords: Haar wavelet method, Differential equation, Operational matrix, Damped forced oscillator}
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This paper investigates existence and uniqueness results for the first order fuzzy integro-differential equations. Then numerical results and error bound based on the left rectangular quadrature rule, trapezoidal rule and a hybrid of them are obtained. Finally an example is given to illustrate the performance of the methods.Keywords: Fuzzy integro, differential equation, Discrete solution, Fuzzy quadrature rule}
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International Journal of Mathematical Modelling & Computations, Volume:2 Issue: 4, Autumn 2012, P 299In this paper, we tried to accelerate the rate of convergence in solving second-order Fredholm type Integro-differential equations using a new method which is based on Improved homotopy perturbation method (IHPM) and applying accelerating parameters. This method is very simple and the result is obtained very fast.Keywords: Improved homotopy perturbation method, Laplace transform, Fredholm integro, differential equation}
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Semidiscrete finite element approximation of a hyperbolic type integro-differential equation is studied. The model problem is treated as the wave equation which is perturbed with a memory term. Stability estimates are obtained for a slightly more general problem. These، based on energy method، are used to prove optimal order a priori error estimates. Keywords: finite element method, wave equation, ý ýintegro, differential equation, stability, a priori error estimate}
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International Journal of Mathematical Modelling & Computations, Volume:2 Issue: 2, Spring 2012, P 127In this paper, we propose a method to approximate the solution of a linear Fredholm integro-differential equation by using the Chebyshev wavelet of the first kind as basis. For this purpose, we introduce the first Chebyshev operational matrix of integration. Chebyshev wavelet approximating method is then utilized to reduce the integro-differential equation to a system of algebraic equations. Illustrative examples are included to demonstrate the advantages and applicability of the technique.Keywords: Integro, differential equation, Chebyshev wavelet of the first kind, Operational matrix of integration, Legendre wavelet, CAS wavelet}
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