Iterative algorithm for parabolic and hyperbolic PDEs with nonlocal boundary conditions

In this paper, we are concerned with the numerical solutions for the parabolic and hyperbolic partial differential equations with nonlocal boundary conditions. Thus, we presented a new iterative algorithm based on the Restarted Adomian Decomposition Method (RADM) for solving the two equations of different types involving dissimilar boundary and nonlocal conditions. The algorithm presented transforms the given nonlocal initial boundary value problem to a local Dirichlet one and then employs the RADM for the numerical treatment. Numerical comparisons were made between our proposed method and the Adomian Decomposition Method (ADM) to demonstrate the efficiency and performance of the proposed method. Keywords: Adomian Decomposition Method, Restarted method, Parabolic and hyperbolic PDEs, Nonlocal boundary condition