Computational DIQM Scheme for Solving Nonlinear Volterra Integro-Differential Equations

Abstract

The authors in this work develop the differential quadrature method (DQM) to solve the nonlinear Volterra integro-differential equation by introducing an integration matrix operator that is fully combined with the differentiation matrix in (DQM) method. The obtained method (DIQM) transforms the discretized nonlinear Volterra integro-differential equation into a nonlinear algebraic system of equations which is solved iteratively by Newton's method. The efficiency of the (DIQM) method is examined by solving three examples where the error norms and convergence rates achieve the expected exponential behaviour.