Asymptotic solvers for ordinary differential equations with multiple frequencies

作者：Condon Marissa; Deano Alfredo; Gao Jing^*; Iserles Arieh

来源：Science China Mathematics, 2015, 58(11): 2279-2300.

DOI：10.1007/s11425-015-5066-5

• highly oscillatory problems
• ordinary differential equation
• modulated Fourier expansions
• multiple frequencies
• numerical analysis

We construct asymptotic expansions for ordinary differential equations with highly oscillatory forcing terms, focusing on the case of multiple, non-commensurate frequencies. We derive an asymptotic expansion in inverse powers of the oscillatory parameter and use its truncation as an exceedingly effective means to discretize the differential equation in question. Numerical examples illustrate the effectiveness of the method.

• 出版日期2015-11
• 单位西安交通大学