New Numerical Method for Solving Eigenvalue Problems Described by Coupled Second-Order Differential Equations

抄録

A systematic iteration scheme is presented to numerically solve the eigenvalue problem described by a coupled set of second-order differential equations under the boundary conditions that the solution is localized near the origin. The method consists of the application of Newton’s iteration scheme to the shooting method. A useful analytical expression for the correction to the trial eigenvalue is obtained. Application is made for two examples, simple harmonic oscillator and electro-magnetic drift-wave in a finite-β plasma in a sheared magnetic field, to demonstrate a remarkable stability, efficiency and accuracy of the method. In the latter example, reduction of the CPU time by factor 20–30 is obtained as compared with the standard simplex method.