Related papers: A Stable Explicit Scheme for Solving Inhomogeneous…
A numerical explicit method to evaluates transient solutions of linear partial differential non-homogeneous equation with constant coefficients is proposed.
We present a general formula for the particular solution of an inhomogeneous linear difference equation with variable coefficients. The answer is expressed as a weighted sum of fundamental solutions of the associated linear difference…
We provide explicit representations of Green's functions for general linear fractional differential operators with {\it variable coefficients} and Riemann-Liouvilles derivatives. We assume that all their coefficients are continuous in $[0,…
A method for enhancing the stability and robustness of explicit schemes in computational fluid dynamics is presented. The method is based in reformulating explicit schemes in matrix form, which cane modified gradually into semi or…
In this paper, a class of finite difference numerical techniques is presented to solve the second-order linear inhomogeneous damped wave equation. The consistency, stability, and convergences of these numerical schemes are discussed. The…
In this work, we study nonlocal differential equations with particular focus on those with reflection in their argument and piecewise constant dependence. The approach entails deriving the explicit expression of the solution to the linear…
In this paper a novel method to solve the constant coefficient wave equation, subject to interface jump conditions, is presented. In general, such problems pose issues for standard finite difference solvers, as the inherent discontinuity in…
This work presents a space-time isogeometric analysis of biharmonic wave problem, in contrast to the more common application of space-time methods to second order wave equations. We first establish the unique solvability of the continuous…
A numerical method to solve the fractional diffusion equation, which could also be easily extended to many other fractional dynamics equations, is considered. These fractional equations have been proposed in order to describe anomalous…
It is well known that second order homogeneous linear ordinary differential equations with slowly varying coefficients admit slowly varying phase functions. This observation underlies the Liouville-Green method and many other techniques for…
In this paper, we present a fast multipole method (FMM) for the half-space Green's function in a homogeneous elastic half-space subject to zero normal stress, for which an explicit solution was given by Mindlin (1936). The image structure…
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…
Explicit time stepping schemes are popular for linear acoustic and elastic wave propagation due to their simple nature which does not require sophisticated solvers for the inversion of the stiffness matrices. However, explicit schemes are…
In this work we revise the most recent developments concerning the study of first order problems regarding differential equations with involutions. We take into account two cases: the case of initial conditions and constant coefficients and…
In this work, an efficient approximation scheme has been proposed for getting accurate approximate solution of nonlinear partial differential equations with constant or variable coefficients satisfying initial conditions in a series of…
Conventional finite-difference schemes for solving partial differential equations are based on approximating derivatives by finite-differences. In this work, an alternative theory is proposed which view finite-difference schemes as…
In this work, we give the general solution sequential linear conformable fractional differential equations in the case of constant coefficients for {\alpha}(\in)(0,1]. In homogeneous case, we use a fractional exponential function which…
Fractional calculus is a powerful and effective tool for modelling nonlinear systems. The M derivative is the generalization of alternative fractional derivative. This M derivative obey the properties of integer calculus. In this paper, we…
In this article, a numerical scheme is introduced for solving the fractional partial differential equation (FPDE) arising from electromagnetic waves in dielectric media (EMWDM) by using an efficient class of finite difference methods. The…
The aim of this paper is to develop and analyze numerical schemes for approximately solving the backward problem of subdiffusion equation involving a fractional derivative in time with order $\alpha\in(0,1)$. After using quasi-boundary…