In this paper, we use modified Laplace decomposition method to solving initial value problems (IVP) of the second order ordinary differential equations. Theproposed method can be applied to linear and nonlinearproblems    

The main idea behind the Laplace transformation is that we can solve an equation (or system of equations) containing differential and integral terms by transforming the equation in time (t) domain into Laplace (2) domain. For example, we can use Laplace transforms to turn an initial value problem into an algebraic problem which is easier to solve. After we solved the problem in Laplace domain w...

We study the eigenvalues of the discrete Schrödinger operator with a complex potential. We obtain bounds on the total number of eigenvalues in the case where V decays exponentially at infinity.

Recently, various applications have motivated the study of spectral structures (eigenvalues and eigenfunctions) of the so-called Laplace-Beltrami operator of a manifold and their discrete versions. A popular choice for the discrete version is the so-called Gaussian weighted graph Laplacian which can be applied to point cloud data that samples a manifold. Naturally, the question of stability of ...

An upwind difference approximation is used for a singularly perturbed problem in material science. Based on the discrete Green’s function theory, the error estimate in maximum norm is achieved, which is first-order uniformly convergent with respect to the perturbation parameter. The numerical experimental result is verified the valid of the theoretical analysis. Keywords—singularly perturbed, u...

Pseudo-Laplace transform is an important notion from pseudo-analysis’ framework that is often used in dealing with differential or integral equation. The (⊕, ̄)-Laplace transform considered here is a generalization of the pseudo-Laplace transform based on a special class of generalized pseudo-operations that need not be commutative nor associative. This pseudo-Laplace type transform has been use...

Starting with a general definition of the Laplace transform on arbitrary time scales, we specify the Laplace transform on isolated time scales, prove several properties of the Laplace transform in this case, and establish a formula for the inverse Laplace transform. The concept of convolution is considered in more detail by proving the convolution theorem and a discrete analogue of the classica...

Partial-post Laplace barriers have been postulated as a means to allow electrowetting transport and geometrical reshaping of fluids, followed by the preservation of fluid geometry after the electrowetting voltage is removed. Reported here is the first investigation of Laplace barriers with the arrayed electrodes and splitting/merging transport functions for an electrowetting lab-on-a-chip. Lapl...

We propose a standard approach to make inference for spatial generalized linear mixed models using Laplace approximation. Based on analysis of two datasets previous analysed in literature, we compare our approach with different approaches. The first the rhizoctonia root rot dataset is an example of Binomial SGLMM and the second rongelap dataset is an example of Poisson or Negative Binomial SGLM...