An operational matrix method for solving a class of nonlinear Volterra integral equations arising in steady activation of a skeletal muscle

Abstract

The problem of the steady activation of a skeletal muscle is one of the ap-plicable phenomena in real life that can be modeled by a Volterra integral equation. The current research aims to investigate this problem by using an effective operational matrix-based method. For this purpose, the opera-tional matrix of integration is derived for the barycentric rational cardinal basis functions. Then, by utilizing the obtained operational matrix and without using any collocation points, the governing integral equation is re-duced to a system of nonlinear algebraic equations. Convergence analysis of the proposed numerical method is studied thoroughly. Moreover, the obtained numerical results based on the proposed method with acceptable computational times support the theoretical results and reveal the accuracy and efficiency of the method.

Keywords

• volterra integral equations
• linear barycentric rational inter-polants
• operational matrix