in this paper, we apply the laplace decomposition method to obtain a series solutions of the burgers-huxley and burgers-fisher equations. the technique is based on the application of laplace transform to nonlinear partial differential equations. the method does not need linearization, weak nonlinearity assumptions or perturbation theory and the nonlinear terms can be easily handled by using the...

A meshless method based on the local Petrov-Galerkin approach is proposed for the solution of steady-state and transient heat conduction problems in a continuously nonhomogeneous anisotropic medium. The Laplace transform is used to treat the time dependence of the variables for transient problems. The analyzed domain is covered by small subdomains with a simple geometry. A weak formulation for ...

Meshless methods based on the local Petrov-Galerkin approach are proposed for solution of steady and transient heat conduction problem in a continuously nonhomogeneous anisotropic medium. Fundamental solution of the governing partial differential equations and the Heaviside step function are used as the test functions in the local weak form. It is leading to derive local boundary integral equat...

The equations for EM dipole near and far radiation fields are formulated for the complex frequency domain with a Laplace Transform analysis for Hertzian dipoles. An s-domain pulsed current source function from ordinary circuit analysis is used in the expressions, and is augmented as needed to refine the pulse. This formulation allows a lucid pole-zero treatment of the field transfer function, y...

this paper presents an analytical model characterizing unsteady groundwater flow in an unconfined aquifer resting on a sloping impervious bed. the aquifer is in contact with a constant water level at one end. the other end is connected to a stream whose level is increasing form an initial level to a final level at a known exponentially decaying function of time. moreover, the aquifer is repleni...

Algebraic techniques based on Laplace transform are widely used for solving differential equations and evaluating transfer of signals while analyzing physical aspects of many safety-critical systems. To facilitate formal analysis of these systems, we present the formalization of Laplace transform using the multivariable calculus theories of HOL-Light. In particular, we use integral, differentia...

In the present paper the authors introduce the exponential integral transform and the complementary error transform, then it is shown that the third iterate of the Laplace transform is the exponential integral transform and a modified third iterate of the Laplace transform is the complementary error transform. Some identities involving these new transforms, the Laplace transform and the Stieltj...

The study of the Laplace operator and its corresponding eigenvalue problem is crucial to understand the foundations of 3D shape analysis. For that reason the most important mathematical properties of the Laplace operator in Euclidean spaces, its eigenvalues and eigenfunctions are summarized and explained in this report. The basic definitions and concepts of infinite dimensional function spaces,...

In this article, we show that Laplace transform can be applied to fractional system. To this end, solutions of linear fractional-order equations are first derived by a direct method, without using Laplace transform. Then the solutions of fractional-order differential equations are estimated by employing Gronwall and Hölder inequalities. They are showed be to of exponential order, which are nece...

For a skip-free Markov process on Z + with generator matrix Q, we evaluate the joint Laplace transform of the occupation times before hitting the state n (starting at 0). This Laplace transform has a very straightforward and familiar expression. We investigate the properties of this Laplace transform, especially the conditions under which the occupation times form a Markov chain.