In this paper, a new algorithm is presented to approximate the solution of a singularly perturbed boundary value problem with leftlayer based on the homotopy perturbation technique and applying the Laplace transformation. The convergence theorem and the error bound of the proposed method are proved. The method is examined by solving two examples. The results demonstrate the reliability and effi...

A general algebraic method of quantum corrections evaluation is presented. Quantum corrections to a few classical solutions (kinks and periodic) of Ginzburg-Landau (phiin-quadro) and Sin-Gordon models are calculated in arbitrary dimensions. The Green function for heat equation with a soliton potential is constructed by means of Laplace transformation theory and Hermit equation for the Green fun...

We consider the discretization in time of a fractional order diffusion equation. The approximation is based on a further development of the approach of using Laplace transformation to represent the solution as a contour integral, evaluated to high accuracy by quadrature. This technique reduces the problem to a finite set of elliptic equations with complex coefficients, which may be solved in pa...

We study the existence and nonexistence of positive (super) solutions to the nonlinear p-Laplace equation −∆pu− μ |x|p u = C |x|σ u in exterior domains of R (N ≥ 2). Here p ∈ (1,+∞) and μ ≤ CH , where CH is the critical Hardy constant. We provide a sharp characterization of the set of (q, σ) ∈ R such that the equation has no positive (super) solutions. The proofs are based on the explicit const...

We study N=2(4) superstring backgrounds which are four-dimensional nonKählerian with non-trivial dilaton and torsion fields. In particular we consider the case that the backgrounds possess at least one U(1) isometry and are characterized by the continual Toda equation and the Laplace equation. We obtain a string background associated with a non-trivial solution of the continual Toda equation, w...

We apply a recently proposed approximation method to the evaluation of non-Gaussian integral and anharmonic oscillator. The method makes use of the truncated perturbation series by recasting it via the modified Laplace integral representation. The modification of the Laplace transformation is such that the upper limit of integration is cut off and an extra term is added for the compensation. Fo...

A parallel numerical algorithm is introduced and analyzed for solving inhomogeneous initial-boundary value parabolic problems. The scheme is based on the method recently introduced in [8] for homogeneous problems. We give a method based on a suitable choice of multiple parameters. Our scheme allows to compute solutions in a wide range of time. Instead of using standard time-marching method, whi...

The Laguerre method for numerically inverting Laplace transforms is an old established method based on the 1935 Tricomi-Widder theorem, which shows (under suitable regularity conditions) that the desired function can be represented as a weighted sum of Laguerre functions, where the weights are coefficients of a generating function constructed from the Laplace transform using a bilinear transfor...