A simple convergent solver for initial value problems
Rafael G. Campos, Francisco Dominguez Mota
TL;DR
This paper introduces a stable, convergent implicit method for solving initial value problems using differentiation matrices from Lagrange interpolation, effective for mildly stiff and complex-plane differential equations.
Contribution
The paper presents a novel, easy-to-use implicit multistep-like solver based on differentiation matrices, extending applicability to complex plane problems.
Findings
Performs well on mildly stiff problems
Stable and convergent for initial value problems
Applicable to differential equations in the complex plane
Abstract
We present a stable and convergent method for solving initial value problems based on the use of differentiation matrices obtained by Lagrange interpolation. This implicit multistep-like method is easy-to-use and performs pretty well in the solution of mildly stiff problems and it can also be applied directly to differential problems in the complex plane.
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Taxonomy
TopicsNumerical methods for differential equations · Electromagnetic Simulation and Numerical Methods · Advanced Numerical Methods in Computational Mathematics