An uncoupled numerical scheme for the equations of nonlinear one-dimensional thermoelasticity

An Efficient Numerical Scheme for Coupled Nonlinear Burgers’ Equations

In this paper, coupled nonlinear Burgers’ equations are solved through a variety of meshless methods known as multiquadric quasi-interpolation scheme. In this scheme, the extension of univariate quasi-interpolation method is used to approximate the unknown functions and their spatial derivatives and the Taylor series expansion is used to discretize the temporal derivatives. The multiquadric qua...

Numerical Methods for One-Dimensional Aggregation Equations

We focus in this work on the numerical discretization of the one dimensional aggregation equation ∂tρ + ∂x(vρ) = 0, v = a(W ′ ∗ ρ), in the attractive case. Finite time blow up of smooth initial data occurs for potential W having a Lipschitz singularity at the origin. A numerical discretization is proposed for which the convergence towards duality solutions of the aggregation equation is proved....

A Numerical Scheme for Solving Nonlinear Fractional Volterra Integro-Differential Equations

In this paper, a Bernoulli pseudo-spectral method for solving nonlinear fractional Volterra integro-differential equations is considered. First existence of a unique solution for the problem under study is proved. Then the Caputo fractional derivative and Riemman-Liouville fractional integral properties are employed to derive the new approximate formula for unknown function of the problem....

Propagation of Singularities in One-dimensional Thermoelasticity Propagation of Singularities in One-dimensional Thermoelasticity

The propagation of singularities for the system of homogeneous thermoelasticity in one space dimension is studied. Linear and a class of semilinear Cauchy problems are considered.

An Opertional Method for The Numerical Solution of Two Dimensional Linear Fredholm Integral Equations With an Error Estimation