Solution Of Volterra-Fredholm Integro-differential Equations Research Articles

A Numerical Method using Collocation Approach for the Solution of Volterra-Fredholm Integro-Differential Equations

This paper consider collocation approach for the numerical solution of Volterra-Fredholm Integro-differential equation using collocation method. We transformed the problem into a system of linear algebraic equations and matrix inversion is adopted to solve the algebraic equations. We substituted the solution algebraic equations into the approximate equation to obtain the numerical result. Some numerical problems are solved to demonstrate the efficiency and consistency of the method.

On the Numerical Solution of Volterra-Fredholm Integro-Differential Equations via Rational Chebyshev Spectral Collocation Approach

On the Numerical Solution of Volterra-Fredholm Integro-Differential Equations via Rational Chebyshev Spectral Collocation Approach

A new operational matrix of Muntz-Legendre polynomials and Petrov-Galerkin method for solving fractional Volterra-Fredholm integro-differential equations

This manuscript is devoted to present an efficient numerical method for finding numerical solution of Volterra-Fredholm integro-differential equations of fractional-order. The technique is based on the M{u}ntz-Legendre polynomials and Petrov-Galerkin method. A new Riemann-Liouville operational matrix for M{u}ntz-Legendre polynomials is proposed using Laplace transform. Employing this operational matrix and Petrov-Galerkin method, the problem transforms to a system of algebraic equations. Next, we solve this system by applying any iterative method. An estimation of the error is proposed. The efficiency and accuracy of the present scheme is illustrated using several examples.

A new method for the solution of Volterra-Fredholm integro-differential equations

In the present study, we investigate the hybrid of Taylor series and Block pulse functions solutions of higher order linear integro-differential Volterra-Fredholm equations (IDVFE) by using a new method. This method transforms IDVFE into the matrix equations which correspond to a system of linear algebraic equations. Some numerical results are also given to illustrate the efficiency of the method.

Approximate solutions of Volterra-Fredholm integro-differential equations of fractional order

In this study, sinc-collocation method is introduced for solving Volterra-Fredholm integrodifferential equations of fractional order. Fractional derivative is described in the Caputo sense. Obtained results are given to literature as a new theorem. Some numerical examples are presented to demonstrate the theoretical results.