In this paper, we aim to make a combination of improved formula for the inverse operator of Lesnic with modified decomposition method for solving initial-boundary value problems and to obtain an approximate solution for partial differential equations with Dirichlet boundary conditions. The combined method is capable of handling both linear and nonlinear equations of boundary value problems and initial-boundary value problems. Approximate analytical solution using an alternative combination of the initial and boundary conditions shows the effectiveness of using Lesnic’s approach over the standard Adomian decomposition method (ADM), also it reduces the size of computational work while still maintaining high accuracy of the numerical solution. Illustrative examples will be examined to support the proposed analysis.

initial-boundary value problems, Lesnic’s approach, Dirichlet boundary conditions, nonlinear partial differential equations, Adomian decomposition method.