A new coupled reduced alternating group explicit method for nonlinear singular two-point boundary value problems on a variable mesh

被引：2
作者：
Mohanty R.K. [1 ]
Talwar J. [2 ]
机构：
[1] Department of Applied Mathematics, South Asian University Akbar Bhawan, Chanakyapuri, 110021, New Delhi
[2] Department of Mathematics, University of Delhi, Delhi
来源：
Numerical Analysis and Applications | 2015年 / 8卷 / 1期
关键词：
Burgers; equation; CRAGE method; geometric mesh; Newton-CRAGE method; RMS errors; singular equation; third-order method; two-point singular boundary value problems;
D O I：
10.1134/S1995423915010061
中图分类号：
学科分类号：
摘要：
In this paper, we discuss a new coupled reduced alternating group explicit (CRAGE) and Newton-CRAGE iteration methods to solve the nonlinear singular two-point boundary value problems u″ = f(r, u, u′), 0 < r < 1 subject to given natural boundary conditions u(0) = A1, u(1) = A2 where A1 and A2 are finite constants, along with a third-order numerical method on a geometric mesh. The proposed method is applicable to singular and nonsingular problems. We have discussed the convergence of the CRAGE iteration method in detail. The results obtained from the proposed CRAGE iteration method are compared with the results of the corresponding two-parameter alternating group explicit (TAGE) iteration methods to demonstrate computationally the efficiency of the proposed method. © 2015, Pleiades Publishing, Ltd.
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页码：55 / 67
页数：12
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共 20 条
  • [1] Keller H.B., Numerical Methods for Two-Point Boundary-Value Problems, (1968)
  • [2] Jain M.K., Iyengar S.R.K., Subramanyam G.S., Variable Mesh Methods for the Numerical Solution of Two-Point Singular Perturbation Problems, Comput. Meth. Appl. Mech. Eng., 42, pp. 273-286, (1984)
  • [3] Evans D.J., Group Explicit Methods for Solving Large Linear Systems, Int. J. Comput.Math., 17, pp. 81-108, (1985)
  • [4] Chawla M.M., Shivakumar P.N., An Efficient Finite Difference Method for Two-Point Boundary Value Problems, Neural Parallel Sci. Comput., 4, pp. 387-396, (1996)
  • [5] Evans D.J., Iterative Methods for Solving Non-Linear Two-Point Boundary Value Problems, Int. J. Comput. Math., 72, pp. 395-401, (1999)
  • [6] Evans D.J., The Solution of Periodic Parabolic Equations by the Coupled Alternating Group Explicit (CAGE) Iterative Method, Int. J. Comput. Math., 4, pp. 227-235, (1990)
  • [7] Evans D.J., Parallel Strategies for Linear Systems of Equations, Int. J. Comput. Math., 81, pp. 417-446, (2004)
  • [8] Sukon K.S., Evans D.J., Two-Parameter AGE (TAGE) Method for the Solution of a Tri-Diagonal Linear System of Equations, Int. J. Comput. Math., 60, pp. 265-278, (1996)
  • [9] Mohanty R.K., Evans D.J., Highly Accurate Two-Parameter CAGE Parallel Algorithms for Non-Linear Singular Two-Point Boundary Value Problems, Int. J. Comput. Math., 82, pp. 433-444, (2005)
  • [10] Mohanty R.K., A Family of Variable Mesh Methods for the Estimates of (du/dr) and Solution of Non-Linear Two-Point Boundary Value Problems with Singularity, J. Comp. Appl. Math., 182, pp. 173-187, (2005)
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