Gautschi-type Integrator Factor Fourier Pseudospectral Method For Two Wave Equations

Boussinesq paradigm equation and Zakharov wave equations are two importantwave propagation models. In this paper, Gautschi-type integrator factor Fourier pseu-dospectral method is proposed to solve the one dimensional Boussinesq paradigm e-quation and one dimensional coupled Zakharov wave equations associated with theperiodic initial boundary values. We get two fully explicit schemes of these two kind-s of wave equations through the above method. And for the scheme of Boussinesqparadigm equation with the condition of τ(?)h, we find that it is spectral-order ofaccuracy in space and second-order of accuracy in time by the mathematical inductionmethod. Similarly, we get the same results for the scheme of zakharov equations on thecondition of τ(?)ε~2h. Moreover, we get that the discrete energy error of the coupledZakharov wave equations is also spectral-order of accuracy in space and second-orderof accuracy in time, and it has an inverse relationship with ε2. Finally, the numericalexperiments are given to verify the correctness of the theoretical proof and the effec-tiveness of the method. In addition, we simulate the propagation of single solitarywave and the collision of two solitary waves through the numerical method.