Electron. J. Diff. Equ.,
Vol. 2015 (2015), No. 28, pp. 1-11.
Numerical solutions for Volterra integro-differential forms of
Lane-Emden equations of first and second kind using Legendre multi-wavelets
Prakash Kumar Sahu, Santanu Saha Ray
Abstract:
A numerical method based on Legendre multi-wavelets is applied for solving
Lane-Emden equations which form Volterra integro-differential equations.
The Lane-Emden equations are converted to Volterra integro-differential
equations and then are solved by the Legendre multi-wavelet method.
The properties of Legendre multi-wavelets are first presented.
The properties of Legendre multi-wavelets are used to reduce the system of
integral equations to a system of algebraic equations which can be solved
by any numerical method. Illustrative examples are discussed to show
the validity and applicability of the present method.
Submitted June 23, 2014 Published January 29, 2015.
Math Subject Classifications: 45D05, 45J05.
Key Words: Legendre multi-wavelet; Volterra integral equation;
integro-differential equation; Lane-Emden equation.
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Prakash Kumar Sahu
National Institute of Technology Rourkela
Department of Mathematics
Rourkela, Odisha-769008, India
email: prakash.2901@gmail.com
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Santanu Saha Ray
National Institute of Technology Rourkela
Department of Mathematics
Rourkela, Odisha-769008, India
email: santanusaharay@yahoo.com
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