chebyshev cardinal functions for solving volterra-fredholm integrodifferential equations using operational matrices

Chebyshev cardinal functions for solving volterra-fredholm integro- differential equations using operational matrices

In this paper, an effective direct method to determine the numerical solution of linear and nonlinear Fredholm and Volterra integral and integro-differential equations is proposed. The method is based on expanding the required approximate solution as the elements of Chebyshev cardinal functions. The operational matrices for the integration and product of the Chebyshev cardinal functions are des...

chebyshev cardinal functions: an effective tool for solving nonlinear volterra and fredholm integro-differential equations of fractional order

a computational method for numerical solution of a nonlinear volterra and fredholm integro-differentialequations of fractional order based on chebyshev cardinal functions is introduced. the chebyshev cardinaloperational matrix of fractional derivative is derived and used to transform the main equation to a system ofalgebraic equations. some examples are included to demonstrate the validity and ...

Ulam stabilities for nonlinear Volterra-Fredholm delay integrodifferential equations

In the present research paper we derive results about existence and uniqueness of solutions and Ulam--Hyers and Rassias stabilities of nonlinear Volterra--Fredholm delay integrodifferential equations. Pachpatte's inequality and Picard operator theory are the main tools that are used to obtain our main results. We concluded this work with applications of ob...

Fuzzy bivariate Chebyshev method for solving fuzzy Volterra-Fredholm integral equations

A rational Chebyshev functions approach for Fredholm-Volterra integro-differential equations

The purpose of this study is to present an approximate numerical method for solving high order linear Fredholm-Volterra integro-differential equations in terms of rational Chebyshev functions under the mixed conditions. The method is based on the approximation by the truncated rational Chebyshev series. Finally, the effectiveness of the method is illustrated in several numerical examples. The p...

The Convergence Study of the Homotopy Analysis Method for Solving Nonlinear Volterra-Fredholm Integrodifferential Equations

We aim to study the convergence of the homotopy analysis method (HAM in short) for solving special nonlinear Volterra-Fredholm integrodifferential equations. The sufficient condition for the convergence of the method is briefly addressed. Some illustrative examples are also presented to demonstrate the validity and applicability of the technique. Comparison of the obtained results HAM with exac...