Authors : Maan A. Rasheed and Mustafa A. Sabri
Abstract: This study is concerned with Laplace transform and its applications to partial differential equations. We derive the general Laplace inversion formula using some complex analysis results. Furthermore, we apply this formula to find the formal solution of a heat conduction problem which is heat equation with Neumann boundary conditions. We conclude that Laplace transforms with the inversion formula provide a potent technique for solving partial differential equations.
Maan A. Rasheed and Mustafa A. Sabri, 2019. Deriving the General Laplace Inversion Formula using Complex Integration Results and its Applications in Solving Partial Differential Equations. Journal of Engineering and Applied Sciences, 14: 3455-3462.