Discrete Galerkin Method for Higher Even-Order Integro-Differential Equations with Variable Coefficients

discrete galerkin method for higher even-order integro-differential equations with variable coefficients

this paper presents discrete galerkin method for obtaining the numerical solution of higher even-order integro-differential equations with variable coefficients. we use the generalized jacobi polynomials with indexes corresponding to the number of homogeneous initial conditions as natural basis functions for the approximate solution. numerical results are presented to demonstrate the effectiven...

An Approximate Method for System of Nonlinear Volterra Integro-Differential Equations with Variable Coefficients

In this paper, we apply the differential transform (DT) method for finding approximate solution of the system of linear and nonlinear Volterra integro-differential equations with variable coefficients, especially of higher order. We also obtain an error bound for the approximate solution. Since, in this method the coefficients of Taylor series expansion of solution is obtained by a recurrence r...

an approximate method for system of nonlinear volterra integro-differential equations with variable coefficients

in this paper, we apply the differential transform (dt) method for finding approximate solution of the system of linear and nonlinear volterra integro-differential equations with variable coefficients, especially of higher order. we also obtain an error bound for the approximate solution. since, in this method the coefficients of taylor series expansion of solution is obtained by a recurrence r...

A Discontinuous Galerkin Method for Higher-order Differential Equations

In this paper we propose a new discontinuous finite element method for higher-order initial value problems where the finite element solution exhibits an optimal O(∆tp+1) convergence rate in the L2 norm. We further show that the p-degree discontinuous solution of differential equation of order m and its first m−1 derivatives are O(∆t2p+2−m) superconvergent at the end of each step. We also establ...

Legendre-Galerkin method for the linear Fredholm integro-differential equations

The Petrov-Galerkin Method and Chebyshev Multiwavelet Basis for Solving Integro-Differential Equations

 Abstract: There are some methods for solving integro-differential equations. In this work, we solve the general-order Feredholm integro-differential equations. The Petrov-Galerkin method by considering Chebyshev multiwavelet basis is used. By using the orthonormality property of basis elements in discretizing the equation, we can reduce an equation to a linear system with small dimension. For ...