The Chebyshev Collocation Method for Finding the Eigenvalues of Fourth-Order Sturm-Liouville Problems

Abstract

In this work, we have suggested that the Chebyshev collocation method can be employed for detecting the eigenvalues of fourth-order Sturm-Liouville problems. Two examples are presented subsequently. Numerical eventuates indicate that the present method is accurate. Introduction The boundary value problems for ordinary differential equations have a notable role theoretically. Also, they have diverse applications. A great number of physical, biological and chemical phenomena, can be explained through using boundary value problems. In this paper, Chebyshev collocationmethod is used to acquire the solutions for the subsequent fourth order nonsingular Sturm-Liouville problems (q0(x)y ′′(x))′′ + (q1(x)y ′(x))′ + (μv(x)− q2(x))y(x) = 0, a < x < b, (1) or y = F (y(x), y′(x), y′′(x), y′′′(x), μ) (2) or y + p3(x)y ′′′(x) + p2(x)y ′′(x) + p1(x)y ′(x) + (μw(x)− r(x))y(x) = 0 (3) with the four linearly independent homogeneous boundary conditions