Studies on the Method of Orthogonal Collocation IV. Laguerre and Hermite Orthogonal Collocation Method

Orthogonal cubic spline collocation method for the Cahn-Hilliard equation

The Cahn–Hilliard equation plays an important role in the phase separation in a binary mixture. This is a fourth order nonlinear partial differential equation. In this paper, we study the behaviour of the solution by using orthogonal cubic spline collocation method and derive optimal order error estimates. We discuss some computational experiments by using monomial basis functions in the spatia...

Tutorial Orthogonal Collocation on Finite Elements

Solution of Electrohydrodynamic Flow Equation Using an Orthogonal Collocation Method Based on Mixed Interpolation

In this Paper, we have proposed a new weighted residual method known as orthogonal collocation-based on mixed interpolation (OCMI). Mixed interpolation uses the classical polynomial approximation with two correction terms given in the form of sine and cosine function. By these correction terms, we can control the error in the solution. We have applied this approach to a non-linear boundary valu...

Calculation of the steady-state oscillations of a flute model using the orthogonal collocation method

In this paper we exploit the method of numerical continuation combined with orthogonal collocation to determine the steady-state oscillations of a model of flute-like instruments that is formulated as a nonlinear neutral delay differential equation. The delay term in the model causes additional complications in the analysis of the behaviour of the model, in contrast to models of other wind inst...

Generalized Laguerre Polynomials Collocation Method for Solving Lane-Emden Equation

In this paper we propose, a collocation method for solving nonlinear singular Lane-Emden equation which is a nonlinear ordinary differential equation on semi-infnite interval. This approach is based on a generalized Laguerre polynomial collocation method. This method reduces the solution of this problem to the solution of a system of algebraic equations.We also present the comparison of this wo...