Numerical treatment of nonlinear third order mixed boundary value problem

Saumya Ranjan Jena; Guesh Simretab Gebremedhin; Prasanta Kumar Mohanty

Saumya Ranjan Jena School of Applied Sciences,KIIT Deemed to be University,\\ Bhubaneswar-751024, Odisha, India
Guesh Simretab Gebremedhin School of Applied Sciences,KIIT Deemed to be University,\\ Bhubaneswar-751024, Odisha, India
Prasanta Kumar Mohanty School of Applied Sciences,KIIT Deemed to be University,\\ Bhubaneswar-751024, Odisha, India

Abstract

In this note, the approximate solution of non-linear boundary value problems (BVPs) of third ordeer ordinary differential equations(ODEs) with a mixed boundary conditions is proposed using fifth step block method with the help of modified Taylor series scheme(MTSS). In this work MTSS is used to find the shooting constants and the BVPs are converted to initial value problems (IVPs). Further fifth step block method is employed for approximate solution of the ODEs on the definite interval. Two numerical are taken into account in order to show accuracy of the proposed method numerically as well as graphically.