Ninth Step Block Method for Numerical Solution of a Fourth Order Ordinary Differential Equation

Ninth Step Block Method for Numerical Solution of a Fourth Order Ordinary Differential Equation

Saumya R. JenaMinakshi Mohanty Satya K. Mishra 

Department of Mathematics, School of Applied Sciences, KIIT, DT University, Bhubaneswar 751024, Odisha, India

Corresponding Author Email: 
saumyafma@kiit.ac.in
Page: 
47-56
|
DOI: 
https://doi.org/10.18280/ama_a.550202
Received: 
12 April 2018
|
Accepted: 
1 June 2018
|
Published: 
30 June 2018
| Citation

OPEN ACCESS

Abstract: 

In this study a unique style of collocation and interpolation have been used to get a nine step block method for the numerical solution of linear or nonlinear initial value problems of fourth order ordinary differential equations. The present technique has been implemented at the selected mesh points to generate a direct nine step block method. In this paper zero stability, order consistency and convergence have been incorporated as the basic properties and two numerical examples have been considered and compared with ODE45 as well as continuous Linear Multistep Method (LMM)for the numerical results with exact results.

Keywords: 

nine-step block method, power series, interpolation, collocation, ordinary differential equation, stability, order of the method

1. Introduction
2. Construction of the New Method
3. Basic Properties of the Block Method
4. Numerical Examples
5. Conclusion
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