Solution Of Nonlinear Volterra Research Articles

A new computational method for solution of non-linear Volterra–Fredholm integro-differential equations

An approximation method is developed for the solution of high-order non-linear Volterra–Fredholm integro-differential (NVFID) equations under the mixed conditions. The approach is based on the orthogonal Chebyshev polynomials. The operational matrices of integration and product together with the derivative operational matrix are presented and are utilized to reduce the computation of Volterra–Fredholm integro-differential equations to a system of non-linear algebraic equations. Numerical examples illustrate the pertinent features of the method.

Taylor polynomial solution of non-linear Volterra–Fredholm integral equation

A Taylor polynomial method is developed for the approximation of a non-linear Volterra–Fredholm integral equation of the second kind.

On some parameter methods for nonlinear Volterra integral equation

Family of methods depend on a few parameters are introduced for the numerical solution of nonlinear Volterra integral equation of the second kind with logarithmic kernel. Bounds for some of these parameters are determined, so the corresponding methods have infinite stability intervals.

Solving banded and near symmetric systems

In an earlier work by the authors [8], finite difference methods applied to obtain numerical approximations for the solution of nonlinear Volterra integro-differential equations with two point boundary conditions were considered. In [8], the auxiliary conditions required to complete the system, were chosen to preserve the symmetry of the banded system. In general, applying natural auxiliary conditions (NAC) would give rise to a nonsymmetric banded system. In this article, we consider the efficient solving of a linear banded system with a near-symmetric coefficient matrix.