Numerical solution of differential eigenvalue problems with variable coefficients with the Tau-Collocation method

Tau Numerical Solution of Volterra Integro-Differential Equations With Arbitrary Polynomial Bases

An approximate analytical solution of higher-order linear differential equations with variable coefficients using improved rational Chebyshev collocation method

The purpose of this paper is to investigate the use of rational Chebyshev (RC) collocation method for solving high-order linear ordinary differential equations with variable coefficients. Using the rational Chebyshev collocation points, this method transforms the high-order linear ordinary differential equations and the given conditions to matrix equations with unknown rational Chebyshev coeffi...

An Approximate Method for System of Nonlinear Volterra Integro-Differential Equations with Variable Coefficients

In this paper, we apply the differential transform (DT) method for finding approximate solution of the system of linear and nonlinear Volterra integro-differential equations with variable coefficients, especially of higher order. We also obtain an error bound for the approximate solution. Since, in this method the coefficients of Taylor series expansion of solution is obtained by a recurrence r...

Numerical Solution of Eigenvalue Problems with Spectral Transformations

Title of dissertation: NUMERICAL SOLUTION OF EIGENVALUE PROBLEMS WITH SPECTRAL TRANSFORMATIONS Fei Xue, Doctor of Philosophy, 2009 Dissertation directed by: Professor Howard C. Elman Department of Computer Science Institute for Advanced Computer Studies This thesis is concerned with inexact eigenvalue algorithms for solving large and sparse algebraic eigenvalue problems with spectral transforma...

Numerical Solution of Quadratic Eigenvalue Problems with Structure-Preserving Methods

Numerical methods for the solution of large scale structured quadratic eigenvalue problems are discussed. We describe a new extraction procedure for the computation of eigenvectors and invariant subspaces of skew-Hamiltonian/Hamiltonian pencils using the recently proposed skew-Hamiltonian isotropic implicitly restarted Arnoldi method (SHIRA). As an application we discuss damped gyroscopic syste...