A Double Exponentially Convergent Method for Solving ODEs
主 题: A Double Exponentially Convergent Method for Solving ODEs
报告人: Professor Tzon-Tzer Lu (National Sun Yat-sen University)
时 间: 2015-08-06 15:30-16:30
地 点: 理科一号楼1303
The traditional numerical methods for differential equations, including finite difference, finite element, finite volume, boundary element and Runge-Kutta methods, all possess polynomial convergence. Modern methods like spectral method, radial basis, method of fundamental solution and Trefftz method, all have exponential convergence. In this talk we will show some results on super-geometric convergence as a super-convergence of exponential one. We will also present a Newton-like method in power series domain for ODEs. It has the speed of double-exponential convergence, which will be the fastest among all existing numerical ODE methods. Keywords: double-exponential convergence, numerical ODE, Newton-like method, super-convergence, power series
