BibTeX:

@article{IJIRSTV3I1177,
     title={A Numerical Approach for Solving Nonlinear Boundary Value Problems in Finite Domain using Spline Collocation Method},
     author={Nileshkumar A Patel and Dr. Jigisha U Pandya},
     journal={International Journal for Innovative Research in Science & Technology},
     volume={3},
     number={1},
     pages={318--321},
     year={},
     url={http://www.ijirst.org/articles/IJIRSTV3I1177.pdf},
     publisher={IJIRST (International Journal for Innovative Research in Science & Technology)},
}

A collocation method with quartic splines has been developed to solve third order boundary value problems. The proposed method tested on third order nonlinear boundary value problem. The solution of nonlinear boundary value has been obtained linear boundary value problems generated by quasilinearization technique. Numerical results obtained by the present method are in a good agreement with the analytical solutions available in the literature. Based on the Spline Collocation Method, a general approximate approach for obtaining solution to nonlinear boundary value problems in finite domains is proposed. To demonstrate its effectiveness, this approach is applied to solve three point nonlinear problems.

Third order differential equation, Quartic Spline, Hessen berg matrix, Quasilinearization Boundary value problem