Computation of Eigenvalues of Singular Sturm-Liouville Problems using Modified Adomian Decomposition Method
نویسندگان
چکیده
Abstract: In this paper, we present a novel method for computation of eigenvalues and eigenfunctions for a class of singular Sturm-Liouville boundary value problems using modified Adomian decomposition method. The proposed method can be applied to any type of regular as well as singular Sturm-Liouville problems. This current method is capable of finding any n-th eigenvalues and eigenfunctions of the problem. The efficiency of the method is tested by considering four singular and one regular examples and the results are compared with previous known results. The proposed scheme gives eigenvalue and eigenfunction simultaneously. Numerical results show that the method is simple, however powerful and effective.
منابع مشابه
Adomian Decomposition Method for Nonlinear Sturm-liouville Problems
In this paper the Adomian decomposition method is applied to the nonlinear SturmLiouville problem −y + y(t) = λy(t), y(t) > 0, t ∈ I = (0, 1), y(0) = y(1) = 0, where p > 1 is a constant and λ > 0 is an eigenvalue parameter. Also, the eigenvalues and the behavior of eigenfuctions of the problem are demonstrated.
متن کاملComputing Eigenvalues of Singular Sturm-Liouville Problems
We describe a new algorithm to compute the eigenvalues of singular Sturm-Liouville problems with separated self-adjoint boundary conditions for both the limit-circle nonoscillatory and oscillatory cases. Also described is a numerical code implementing this algorithm and how it compares with SLEIGN. The latter is the only effective general purpose software available for the computation of the ei...
متن کاملComputing the Spectrum of Non Self-adjoint Sturm-liouville Problems with Parameter Dependent Boundary Conditions
— This paper deals with the computation of the eigenvalues of non self-adjoint Sturm-Liouville problems with parameter dependent boundary conditions using the regularized sampling method. A few numerical examples among which singular ones will be presented to illustrate the merit of the method and comparison made with the exact eigenvalues when they are available.
متن کاملModified Laplace Decomposition Method for Singular IVPs in the second-Order Ordinary Differential Equations
In this paper, we use modified Laplace decomposition method to solving initial value problems (IVP) of the second order ordinary differential equations. Theproposed method can be applied to linear and nonlinearproblems
متن کاملHomotopy perturbation method for eigenvalues of non-definite Sturm-Liouville problem
In this paper, we consider the application of the homotopy perturbation method (HPM) to compute the eigenvalues of the Sturm-Liouville problem (SLP) which is called non-definite SLP. Two important Examples show that HPM is reliable method for computing the eigenvalues of SLP.
متن کامل