A numerical implementation of higher-order time integration method for the transient heat conduction equation with a moving boundary based on boundary immobilization technique

In this paper, we are proposing an efficient method to solve the transient heat conduction equation with a moving boundary based on the boundary immobilization method (BIM). The transformed problem is semi discretized by the method of lines (MOL), i.e., central finite difference approximation is made for the spatial derivatives. The resultant system of ordinary differential equations applied the strong stability preserving Runge-Kutta methods (SSP-RK43). A transient heat conduction equation with a moving boundary having exact solutions is considered to check the efficiency and accuracy of the numerical schemes. l2 and l∞ error norms are taken to compare numerical results with the corresponding exact solution.