Back
 AM  Vol.2 No.10 , October 2011
High Accuracy Arithmetic Average Discretization for Non-Linear Two Point Boundary Value Problems with a Source Function in Integral Form
Abstract: In this article, we report the derivation of high accuracy finite difference method based on arithmetic average discretization for the solution of Un=F(x,u,u´)+∫K(x,s)ds , 0
Cite this paper: nullR. Mohanty and D. Dhall, "High Accuracy Arithmetic Average Discretization for Non-Linear Two Point Boundary Value Problems with a Source Function in Integral Form," Applied Mathematics, Vol. 2 No. 10, 2011, pp. 1243-1251. doi: 10.4236/am.2011.210173.
References

[1]   H. B. Keller, “Numerical Methods for Two Point Boun-dary Value Problems”, Blaisdell, London, 1968.

[2]   P. J. Davis and P. Rabinowitz, “Method of Numerical Integra-tion,” 2nd Edition, Academic Press, New York, 1970.

[3]   G. M. Phillips, “Analysis of Numerical Itera-tive Methods for Solving Integral and Integro-Differential Equations,” Computer Journal, Vol. 13, No. 3, 1970, pp. 297-300. doi:10.1093/comjnl/13.3.297

[4]   P. Linz, “A Method for Approximate Solution of Linear Integro-Differential Equations,” SIAM Journal on Numerical Analysis, Vol. 11, No. 1, 1974, pp. 137-144. doi:10.1137/0711014

[5]   V. Lakshmikantham and M. R. M. Rao, “Theory of Integro-Differential Equations,” Gordon and Breach, London, 1995.

[6]   K. E. Atkinson, “The Numerical Solution of Integral Equations of the Second Kind,” Cambridge University Press, Cambridge, 1997. doi:10.1017/CBO9780511626340

[7]   R. P. Agarwal and D. O’Regan, “Integral and Integro-Differential Equa-tions: Theory, Method and Applications,” Gordon and Breach, London, 2000.

[8]   M. K. Jain, S. R. K. Iyenger and G. S. Subramanyam, “Variable Mesh Methods for the Numerical Solution of Two Point Singular Perturbation Problems,” Computer Methods in Applied Mechanics and Engineering, Vol. 42, 1984, pp. 273-286. doi:10.1016/0045-7825(84)90009-4

[9]   R. K. Mohanty, “A Family of Variable Mesh Methods for the Estimates of (du/dr) and the Solution of Nonlinear Two Point Boundary Value Problems with Singularity,” Journal of Computational and Applied Mathematics, Vol. 182, No. 1, 2005, pp. 173-187. doi:10.1016/j.cam.2004.11.045

[10]   R. K. Mohanty and N. Khosla, “A Third Order Accurate Variable Mesh TAGE Iterative Method for the Numerical Solution of Two Point Nonlinear Singular Boundary Value Prob-lems,” International Journal of Computer Mathematics, Vol. 82, No. 10, 2005, pp. 1261-1273. doi:10.1080/00207160500113504

[11]   R. K. Mohanty and N. Khosla, “Application of TAGE Iterative Algo-rithms to an Efficient Third Order Arithmetic Average Variable Mesh Discretization for Two Point Non-Linear Boundary Value Problems,” Applied Mathematics and Computations, Vol. 172, No. 1, 2006, pp. 148-162. doi:10.1016/j.amc.2005.01.134

[12]   R. K. Mohanty, “A Class of Non-Uniform Mesh Three Point Arithmetic Av-erage Discretization for and the estimates of ,” Applied Ma-thematics and Computations , Vol. 183, No. 1, 2006, pp. 477-485. doi:10.1016/j.amc.2006.05.071

[13]   R. K. Mohanty and D. Dhall, “Third Order Accurate Variable Mesh Discretization and Application of TAGE Iterative Method for the Non-Linear Two-Point Boundary Value Problems with Homogeneous Functions in Integral Form,” Applied Mathematics and Computations, Vol. 215, 2009, pp. 2024-2034. doi:10.1016/j.amc.2009.07.046

[14]   G. Evans, “Practical Numerical Integration,” John Wiley & Sons, New York, 1993.

[15]   R. S. Varga, “Matrix Iterative Analysis,” Springer-Verlag, Berlin, 2000. doi:10.1007/978-3-642-05156-2

[16]   D. M. Young, “Iterative Solution of Large Linear Systems,” Dover Pub-lication, New York, 2003.

[17]   C. T. Kelly, “Iterative Methods for Linear and Non-linear equations,” SIAM Publication, Philadelphia, 1995.

[18]   D. J. Evans, “Itera-tive Methods for Solving Nonlinear Two Point Boundary Value Problems,” International Journal of Computer Mathematics, Vol. 72, No. 3, 1999, pp. 395-401. doi:10.1080/00207169908804862

 
 
Top