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题目Spectra computation of the highly oscillatory integral equations





摘要:We are concerned with the numerical computation of the spectra of highly oscillatory integrals with Fox-Li integral kernel and the weakly singular absolute oscillator. Discretised using the modified Fourier basis, the spectral problem for the integral equation is converted into two independent infinite systems of linear equations whose unknowns are the coefficients of the modified Fourier functions, namely the cosine and shifted sine functions, respectively. Each (m,n) entry of the resulting coefficient matrices can be represented exactly by expressions involving the special function with an argument that involves the oscillatory parameter ω and the numbers m and n. Moreover, considering the behaviour of the error function for a large argument, the asymptotics for each entry are analysed for large ω or for large m and n and this enables efficient truncation of the infinite systems. Numerical experiments are provided to illustrate the effectiveness of this method.This is a joint work withArieh IserlesandMarissa Condon.

报告人简介:高静,西安交通大学数学与统计学院副教授、硕士研究生导师,英国剑桥大学博士后。主要致力于高振荡现象及其计算、渐近分析和微积分方程数值算法的研究,尤其是来自物理和医学等自然科学中的各类高振荡模型的数值逼近。在Journal of Computational Physics、BIT Numerical Mathematics,Nonlinear Analysis、Journal of Computational and Applied Mathematics、Science China Mathematics、Journal of Computational Mathematics等国际重要学术期刊杂志上发表论文30多篇。同时,主持完成国家自然科学基金2项和教育部博士点专项1项、陕西省工业攻关项目和自然科学基金等各类科研项目3项。

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