Construction and investigation of new numerical algorithms for the heat equation
Kulcsszavak:explicit numerical methods, heat equation, parabolic PDEs, hopscotch method, UPDF
In this paper-series, we use two known, but non-conventional algorithms, the UPFD and the odd-even hopscotch method, to construct new schemes for the numerical solution of the heat equation. In this part of the series, we examine the algorithms analytically. We exactly prove that all the methods are first order time integrators, three of them preserve positivity of the solutions and we deduce important information about the convergence and accuracy of the methods. Numerical case studies will be presented in the next two part of the series.