Numerical methods for computing the eigenvalues of linear fourth-order boundary-value problems
نویسنده
چکیده
Twizell, E.H. and S.A. Matar, Numerical methods for computing the eigenvalues of linear fourth-order boundary-value problems, Journal of Computational and Applied Mathematics 40 (1992) 115-125. Novel finite-difference methods are developed for approximating the cigenvalues of three types of linear, fourth-order, two-point, boundary-value problems. The fourth-order differential equation is transformed into a system of first-order equations and the numerical methods are derived by replacing the matrix exponential function in a recurrence relation by Pade approximants. Numerical results are obtained for a number of problems from the literature.
منابع مشابه
Two New Finite Difference Methods for Computing Eigenvalues of a Fourth Order Linear Boundary Value Problem 525
This paper describes some new finite difference methods of order 2 and 4 for computing eigenvalues of a two-point boundary value problem associated with a fourth order differential equation of the form (py")" + (q r)y 0. Numerical results for two typical eigenvalue problems are tabulated to demonstrate practical usefulness of our methods.
متن کاملMatrix methods for computing eigenvalues of Sturm-Liouville problems of order four
This paper examines and develops matrix methods to approximate the eigenvalues of a fourth order Sturm-Liouville problem subjected to a kind of fixed boundary conditions, furthermore, it extends the matrix methods for a kind of general boundary conditions. The idea of the methods comes from finite difference and Numerov’s method as well as boundary value methods for second order regular Sturm-L...
متن کاملA mathematically simple method based on denition for computing eigenvalues, generalized eigenvalues and quadratic eigenvalues of matrices
In this paper, a fundamentally new method, based on the denition, is introduced for numerical computation of eigenvalues, generalized eigenvalues and quadratic eigenvalues of matrices. Some examples are provided to show the accuracy and reliability of the proposed method. It is shown that the proposed method gives other sequences than that of existing methods but they still are convergent to th...
متن کاملNON-POLYNOMIAL SPLINE SOLUTIONS FOR SPECIAL NONLINEAR FOURTH-ORDER BOUNDARY VALUE PROBLEMS
We present a sixth-order non-polynomial spline method for the solutions of two-point nonlinear boundary value problem u(4)+f(x,u)=0, u(a)=α1, u''(a)= α2, u(b)= β1,u''(b)= β2, in off step points. Numerical method of sixth-order with end conditions of the order 6 is derived. The convergence analysis of the method has been discussed. Numerical examples are presented to illustrate the applications ...
متن کاملAn Effective Numerical Technique for Solving Second Order Linear Two-Point Boundary Value Problems with Deviating Argument
Based on reproducing kernel theory, an effective numerical technique is proposed for solving second order linear two-point boundary value problems with deviating argument. In this method, reproducing kernels with Chebyshev polynomial form are used (C-RKM). The convergence and an error estimation of the method are discussed. The efficiency and the accuracy of the method is demonstrated on some n...
متن کامل