Numerical Solution of a Class of the Nonlinear Volterra Integro-Differential Equations

Abstract

In this paper, we develop the operational Tau method for solving nonlinear Volterra integro-differential equations of the second kind. The existence and uniqueness of the problem is provided. Here, we show that the nonlinear system resulted from the operational Tau method has a semi triangular form, so it can be solved easily by the forward substitution method. Finally, the accuracy of the method is verified by presenting some numerical computations.

Modification of Laplace Adomian Decomposition Method for Solving Nonlinear Volterra Integral and Integro-differential Equations based on Newton Raphson Formula

“…. Table 3 and Figure 3 show that the approximate numerical solution compared with exact [21] is very superior having maximum absolute error 0.003. …”

“…Nonlinear Volterra integral equations arise in many scientific fields such as the population dynamics, spread of epidemics and semi-conductor devices [25]. Volterra integro-differential equations also emanated in many physical applications such as biological species coexisting together with increasing and decreasing rates of generating and in engineering applications such as heat transfer, diffusion process in general [3,4,21,24]. Recently, many researchers investigated the solution of these problems.…”

New Model for Solving Mixed Integral Equation of the First Kind with Generalized Potential Kernel

“…The field of integral and integro-differential equations is a very important subject in applied mathematics, because mathematical formulation of many physical phenomena contains integral and integro-differential equations (Saeedi, L., Tari, A. & Masuleh, S. H., 2013).Integral equations are very important branch of mathematics, which come in application in many physical problems.…”

“…& Masuleh, S. H., 2013).Integral equations are very important branch of mathematics, which come in application in many physical problems. Now, the integral equations have received considerable interest of many applications in different mathematical areas of sciences, for example see (Saeedi, L., Tari, A. & Masuleh, S. H., 2013;Geng, F. Z.…”

A new approach to homotopy perturbation method for solving systems of Volterra integral equations of first kind

“…Applying decomposition method, Ngarasta et al (2009) solved Volterra integral equations system. Saeedi et al (2013) solved some nonlinear Volterra integral equations of the first kind numerically.…”