In this paper, we propose a numerical method for solving fractional partial differential
equations. This method is based on the homotopy perturbation method and Laplace …

This paper discusses the applications of numerical inversion of the Laplace transform
method based on the Bernstein operational matrix to find the solution to a class of fractional …

Abstract The Laplace transform and Laguerre polynomials are applied to the solution of the
Bagley–Torvik equation. We first convert the fractional differential equation into the algebraic …

Matrix multiplication (MM) is a computationally-intensive operation in many algorithms used
in scientific computations. Not only one of the kernels in numerical linear algebra, the …

Laplace transforms are frequently used in the design of control structures for chemical
engineering processes. In this paper, we have developed a novel numerical method to …

This paper is devoted to designing a practical algorithm to invert the Laplace transform by
assuming that the transform possesses the Puiseux expansion at infinity. First, the general …

This paper provides a technique to investigate the inverse Laplace transform by using
orthonormal Bernstein operational matrix of integration. The proposed method is based on …

Piecewise interpolation methods, as spline or Hermite cubic interpolation methods, define
the interpolating function by means of polynomial pieces and ensure that some regularity …

In this study, a numerical approach based on a combination of homotopy perturbation
method and Laplace transform is proposed to find numerical solutions of parabolic partial …

According to the governing wave equations for unsaturated porous media, a theoretical
model is proposed to obtain the transient response solution of single-layer unsaturated …