A Christov Integrating Factor Method for Approximating Rational PDE Solutions

Abstract

Rational solutions of partial differential equations (PDEs) are notoriously difficult to approximate via spectral Fourier methods due to their algebraically slow decay rate. In this work we discuss approximating rational PDE solutions in a basis of orthogonal functions known as the Christov functions, allowing for the computation of its spectrum via the fast Fourier transform. An explicit fourth-order integrating factor method is derived. The effectiveness of the method is tested on several nonlinear PDEs. Relative to a straightforward pseudo-spectral approximation, the integrating factor method supports larger regions of stability resulting in a more efficient scheme.