Use of a shooting method to compute eigenvalues of fourth-order two-point boundary value problems
It is shown how the shooting method (known for solving regular noneigenvalue type two-point boundary value problems) can also be used for solving eigenvalue problems related to fourth-order ordinary differential equations. Only four first-order equations, obtained after rewriting the fourth-order equation, have to be integrated from one end of the shooting range to the other. In the first stage of the procedure approximations to the required eigenvalues are obtained by finding a least-squares solution for various eigenvalues starting with small values near zero and stepping forward to cover the range of interest. The second stage consists of a Newton procedure to compute accurately the required eigenvalue and the corresponding eigenvector. Newton iterations for the first and fifth eigenvalues are tabulated.
fourth-order ordinary differential equations
scientific article; zbMATH DE number 490556