Exponential integrators for second-order in time partial differential equations

TL;DR

This paper introduces efficient exponential integrator methods for solving second-order in time PDEs like wave and beam equations, focusing on computing matrix exponential actions and demonstrating their effectiveness through simulations.

Contribution

The paper develops a novel approach for efficiently computing matrix exponential actions for second-order PDEs, enabling improved numerical solutions.

Findings

Efficient computation of matrix exponential actions for second-order PDEs.

Numerical simulations demonstrating the effectiveness of the proposed methods.

Abstract

Two types of second-order in time partial differential equations (PDEs), namely semilinear wave equations and semilinear beam equations are considered. To solve these equations with exponential integrators, we present an approach to compute efficiently the action of the matrix exponential as well as those of related matrix functions. Various numerical simulations are presented that illustrate this approach.