Related papers: On Methods for Transforming and Solving Finite Ser…
This paper is about a method for solving infinite series in closed form by using inverse and forward Laplace transforms. The resulting integral is to be solved instead. The method is extended by parametrizing the series. A further Laplace…
The author's method (math-ph/9804010) that uses the Laplace transform to find exact values for a large class of convergent series is extended to trigonometric series.
In this article, a new modified Laplace-Fourier method is developed in order to obtain the solutions of linear neutral delay differential equations. The proposed method provides a more accurate solution than the one provided by the pure…
In this paper we show an alternative way of defining Fourier Series and Transform by using the concept of convolution with exponential signals. This approach has the advantage of simplifying proofs of transforms properties and, in our view,…
In this paper, we solve Laplace equation analytically by using differential transform method. For this purpose, we consider four models with two Dirichlet and two Neumann boundary conditions and obtain the corresponding exact solutions. The…
In this note we propose a generalization of the Laplace and Fourier transforms which we call symmetric Laplace transform. It combines both the advantages of the Fourier and Laplace transforms. We give the definition of this generalization,…
Transform methods, like Laplace and Fourier, are frequently used for analyzing the dynamical behaviour of engineering and physical systems, based on their transfer function, and frequency response or the solutions of their corresponding…
Recently, it was found that a new set of simple techniques allow one to conveniently express ordinary integrals through differentiation. These techniques add to the general toolbox for integration and integral transforms such as the Fourier…
In this paper, we introduce a Laplace-type integral transform called the Shehu transform which is a generalization of the Laplace and the Sumudu integral transforms for solving differential equations in the time domain. The proposed…
The article contents suggestions on how to perform the Fast Fourier Transform over Large Finite Fields. The technique is to use the fact that the multiplicative groups of specific prime fields are surprisingly composite.
We discuss exact analytical solutions of a variety of statistical models recently obtained for finite systems by a novel powerful mathematical method, the Laplace-Fourier transform. Among them are a constrained version of the statistical…
In this study, we introduce and explore a delay differential equation that lends itself to explicit solutions in the Fourier-transformed space. Through the careful alignment of the initial function, we can construct a highly accurate…
A finite transformation method is introduced. This method is equivalent to the $Z$ transform method to a certain extent but generalizes it. By applying the presented method to the Bessel functions, it is possible to solve related ordinary…
In this article I present a fast and direct method for solving several types of linear finite difference equations (FDE) with constant coefficients. The method is based on a polynomial form of the translation operator and its inverse, and…
We build convergent discretizations and semi-implicit solvers for the Infinity Laplacian and the game theoretical $p$-Laplacian. The discretizations simplify and generalize earlier ones. We prove convergence of the solution of the Wide…
A novel method for computation of the discrete Fourier transform over a finite field with reduced multiplicative complexity is described. If the number of multiplications is to be minimized, then the novel method for the finite field of…
In this paper we apply the innovative Laplace transformation method introduced by Sheen, Sloan, and Thom\'ee (IMA J. Numer. Anal., 2003) to solve the Black-Scholes equation. The algorithm is of arbitrary high convergence rate and naturally…
We present a method derived from Laplace transform theory that enables the evaluation of fractional integrals. This method is adapted and extended in a variety of ways to demonstrate its utility in deriving alternative representations for…
In this paper, we introduce a novel semi-analytical method for solving a broad class of initial value problems involving differential, integro-differential, and delay equations, including those with fractional and variable-order…
In this paper a new method for inverting the Laplace transform from the real axis is formulated. This method is based on a quadrature formula. We assume that the unknown function $f(t)$ is continuous with (known) compact support. An…