Highly Efficacious Sixth-Order Compact Approach with Nonclassical Boundary Specifications for the Heat Equation

Abstract

This paper suggests an accurate numerical method based on a sixth-order compact difference scheme and explicit fourth-order Runge–Kutta approach for the heat equation with nonclassical boundary conditions (NCBC). According to this approach, the partial differential equation which represents the heat equation is transformed into several ordinary differential equations. The system of ordinary differential equations that are dependent on time is then solved using a fourth-order Runge–Kutta method. This study deals with four test problems in order to provide evidence for the accuracy of the employed method. After that, a comparison is done between numerical solutions obtained by the proposed method and the analytical solutions as well as the numerical solutions available in the literature. The proposed technique yields more accurate results than the existing numerical methods.