A new numerical method for heat equation subject to integral specifications

Abstract

We develop a numerical technique for solving the one-dimensional heat equation that combine classical and integral boundary conditions. The combined Laplace transform, high-precision quadrature schemes, and Stehfest inversion algorithm are proposed for numerical solving of the problem. A Laplace transform method is introduced for solving considered equation, definite integrals are approximated by high-precision quadrature schemes. To invert the equation numerically back into the time domain, we apply the Stehfest inversion algorithm. The accuracy and computational efficiency of the proposed method are verified by numerical examples.