A Novel Hybrid Solving Approach Based on Combining Similarity Solutions with Laplace Transformation Technique to Solve Different Engineering Problems

Abstract

In this study Laplace transformation technique combined with similarity solutions are used to solve PDE involves derivatives with respect to time and two spatial parameters. The hybrid approach is based on transforming the PDE from the real physical time domain to the Laplacian domain. The obtained PDE in the Laplacian domain involves only derivatives with respect to the two spatial parameters. This transformed PDE is then solved by similarity solution approach to convert it from a PDE in the Laplacian domain to an ODE in another domain involves independent parameter consists of the Laplace parameter s and the two independent spatial parameters. A case is discussed to demonstrate the capabilities of the proposed approach in solving different engineering problems.