A Numerical Method for Eigenvalue Problems of Integral Equations

Abstract

A new numerical method for solving an integral equation
F(k)Ψ(k)=∫_−∞^∞dk′ K(k, k′; ω)Ψ(k′)
to obtain eigenvalues ω and the corresponding eigenfunctions Ψ(k) is proposed. The kernel of the integrand K(k, k′; ω) is a complex function with respect to k, k′ and has no particular symmetries. The method is based upon Newton’s iterative method and gives high efficiency in numerical analyses. As an example the problem of the drift wave in a sheared magnetic field is presented.