Computational & Applied Math Seminar

This talk is concerned with the numerical computation of oscillatory integrals involved Gaussian function, and the oscillatory structures of solutions to the integral equations with oscillatory kernels. The integrand involved Gaussian function is a product of a smooth function and the Gaussian function with a small standard deviation. We then study the oscillatory structures of solutions of Volterra integral and integro-differential equations with highly oscillatory kernels. We finally present some effective numerical methods for the integral equations with singular kernels.