Our goal was to find more effective numerical algorithms to solve the heat or diffusion
equation. We created new five-stage algorithms by shifting the time of the odd cells in the …

The Gr\" unwald and shifted Gr\" unwald formulas for the function $ y (x)-y (b) $ are first order
approximations for the Caputo fractional derivative of the function $ y (x) $ with lower limit at …

This paper reports on a novel explicit numerical method for the spatially discretized diffusion
or heat equation. After discretizing the space variables as in conventional finite difference …

This paper introduces a set of new fully explicit numerical algorithms to solve the spatially
discretized heat or diffusion equation. After discretizing the space and the time variables …

We introduce a novel explicit and stable numerical algorithm to solve the spatially
discretized heat or diffusion equation. We compare the performance of the new method with …

In this paper we introduce a new type of explicit numerical algorithm to solve the spatially
discretized linear heat or diffusion equation. After discretizing the space variables as in …

A numerical method based on an integro-differential equation and local interpolating
functions is proposed for solving the one-dimensional wave equation subject to a non-local …

The main objective of this paper is to propose a new boundary element method (BEM)
modeling for stress sensitivity of nonlocal thermo-elasto-plastic damage problems. The …

In this work, two-dimensional inverse quasi-linear parabolic problem with periodic boundary
and integral overdetermination conditions is investigated. The formal solution is obtained by …

In this paper, one-dimensional heat equation subject to both Neumann and Dirichlet initial
boundary conditions is presented and a Homotopy Perturbation Method (HPM) is utilized for …