In the paper, we study approximation properties of the Malmquist-Takenaka-Christov (MTC) system. We show that the discrete MTC approximations converge rapidly under mild restrictions on functions asymptotic at infinity. This makes them particularly suitable for solving semi- and quasi-linear problems containing Fourier multipliers, whose symbols are not smooth at the origin. As a concrete application, we provide rigorous convergence and stability analyses of a collocation MTC scheme for solving the nonlinear Benjamin equation. We demonstrate that the method converges rapidly and admits an efficient implementation, comparable to the best spectral Fourier and hybrid spectral Fourier/finite-element methods described in the literature.

在本文中，我们研究了Malmquist-Takenaka-Christov（MTC）系统的近似性质。我们表明，离散MTC近似在无穷大渐近函数的适度限制下迅速收敛。这使得它们特别适合于解决包含傅立叶乘法器的半线性和准线性问题，该傅立叶乘法器的符号在原点处不平滑。作为一个具体的应用，我们提供了用于求解非线性本杰明方程的搭配MTC方案的严格收敛性和稳定性分析。我们证明了该方法迅速收敛并接受了有效的实现，可与文献中描述的最佳光谱傅里叶和混合光谱傅里叶/有限元方法相媲美。