3 research outputs found
Collocation Method via Jacobi Polynomials for Solving Nonlinear Ordinary Differential Equations
We extend a
collocation method for solving a nonlinear
ordinary differential
equation (ODE) via Jacobi polynomials. To date, researchers
usually use Chebyshev or Legendre collocation method for solving
problems in chemistry, physics, and so forth, see the works of (Doha and Bhrawy 2006, Guo 2000, and Guo et al. 2002). Choosing the optimal polynomial for solving every ODEs problem
depends on many factors, for example, smoothing continuously and
other properties of the solutions. In this paper, we show
intuitionally that in some problems choosing other members of
Jacobi polynomials gives better result compared to Chebyshev or
Legendre polynomials
The Generalized Laguerre Matrix Method or Solving Linear Differential-Difference Equations with Variable Coefficients
In this paper, a new and efficient approach based on the generalized Laguerre matrix method for numerical approximation of the linear differential-difference equations (DDEs) with variable coefficients is introduced. Explicit formulae which express the generalized Laguerre expansion coefficients for the moments of the derivatives of any differentiable function in terms of the original expansion coefficients of the function itself are given in the matrix form. In the scheme, by using this approach we reduce solving the linear differential equations to solving a system of linear algebraic equations, thus greatly simplify the problem. In addition, several numerical experiments are given to demonstrate the validity and applicability of the method