Numerical Simulation of Cable Equation Using Differential Quadrature Method

Neurons play an important role in the study related to the human brain. Circuit model of the membrane is an important mathematical model that helps to understand the functioning of neurons. Generation of this model give rise to a partial differential equation, which becomes famous as Cable equation. This article is the study of numerical solutions of cable equation obtained by the application of differential quadrature method with trigonometric B-spline as basis functions. Quadrature method is a well known numerical method to solve linear and nonlinear partial differential equations. Application of the method reduces the partial differential equation into a system of ordinary differential equations which is solved by the Runge Kutta (RK) method. To validate the accuracy of the proposed scheme two numerical examples are considered and the obtained results have been shown by figures and tables.