Collocation Method for the Solution of Boundary Value Problems
Journal Title: Asian Research Journal of Mathematics - Year 2017, Vol 2, Issue 5
Abstract
In mathematics, collocation method is a method for the numerical solution of ordinary differential, partial differential and integral equations. The idea is to choose a finite-dimensional space of candidate solutions (usually polynomial up to a certain degree) and a number of points in the domain (called collocation points), and to select that solution which satisfies the given equation at the collocation points. A numerical method for solving non-linear two-point boundary value problems was implemented which based on collocation method. Two-point Taylor polynomial of order six was used as trial function to obtain the residual function. The method was implemented on some existing problems solved with other numerical methods to show that the method can be equal used to solve the problem, the results obtained were compared to verify the reliability and accuracy of the method and it was observed that collocation method is more effective in each case because the error is minimal compare with the results obtained with the other numerical methods.
Authors and Affiliations
F. O. Akinpelu, O. J. Alao
Keywords
Related Articles
- EP ID EP338399
- DOI 10.9734/ARJOM/2017/30642
- Views 78
- Downloads 0
The Effect of Chemical Reaction, and Thermal Radiation on Magnetohydrodynamic Casson Fluid Flow over Non-linearly Stretching Surface with Suction
In the present paper, we investigate numerically the effect of chemical reaction, and radiation on magnetohydrodynamic Casson fluid flow over non-linearly stretching surface with fluid suction. By suitable similarity tra...
Maximum Likelihood Estimation in Nonlinear Fractional Stochastic Volatility Model
We study the strong consistency and asymptotic normality of the maximum likelihood estimator (MLE) of a drift parameter in a stochastic volatility model when both the asset price process and the stochastic volatility are...
Steady Oscillatory Flow in a Bifurcating Green Plant
Steady oscillatory flow in a bifurcating green plant is investigated. The channel is assumed axisymmetrical and porous; the fluid is Newtonian, incompressible, electrically conducting and chemically reactive but of the o...
Modelling Volatility of Asset Returns in Nigerian Stock Market: Applications of Random Level Shifts Models
This study examines the impact of structural breaks on conditional variance and mean reversion in symmetric and asymmetric GARCH models. A multiple breakpoint testing procedure was used to identify structural break point...
Conditional Least Squares Estimation for Discretely Sampled Nonergodic Di usions
Strong consistency and conditional asymptotic normality of the conditional least squares estimator of a parameter appearing nonlinearly in the time dependent drift coefficient of the Itˆo stochastic differential equation...