# Numerical Solution of Linear Emden Fowler Boundary Value Problem in Fuzzy Environment

Volume 15, Issue 3, pp 179-194 Publication Date: October 15, 2015
• 1218 Views

### Authors

A. F. Jameel - School of Mathematical Sciences, 11800 USM, University Sains Malaysia, Penang, Malaysia Sarmad A. Altaie - Computer Engineering Department, University of Technology, Baghdad, Iraq

### Abstract

In this paper a numerical method for solving Tow Point Fuzzy Boundary Value Problems '(TPFBVP) involving linear Emden Folwer equation is considered. The finite difference method (FDM) for solving TPFBVP is introduced and the proof of convergence of approximate solutions is brought in detail. Finally a numerical example is solved for illustrating the capability of method.

### Keywords

• Fuzzy numbers
• fuzzy differential equations
• two point fuzzy boundary value problems
• Finite difference method.

•  65L05
•  34A34
•  34A07

### References

• [1] Z. Akbarzadeh Ghanaie, M. Mohseni Moghadam, Solving fuzzy differential equations by Runge-Kutta method, The Journal of mathematics and computer science, 2(2) (2011), 208 – 221.

• [2] M. Rostami, M. Kianpour, E. bashardoust, A numerical algorithm for solving nonlinear fuzzy differential equations, The Journal of mathematics and computer science, 2(4) (2011), 667 – 671.

• [3] R. A. Usmani, Discrete methods for a boundary value problem with engineering applications, Math. Comput., 32 (1978), 1087 – 1096.

• [4] S. Ghosh, D. Roy, Numeric-Analytic Form of the Adomian Decomposition Method for Two-Point Boundary Value Problems in Nonlinear Mechanics, J. Eng. Mech. , 133(10) (2007), 1124-1133.

• [5] T. Ray Mahapatra, A. S. Gupta, Heat transfer in stagnation-point flow towards a stretching sheet, Heat and Mass Transfer., 38(6) (2002), 517-52.

• [6] R. Sharma, A. Ishak, I. Pop, Partial Slip Flow and Heat Transfer over a Stretching Sheet in a Nano fluid, http://dx.doi.org/10.1155/2013/724547. , 2013 (2013), 7 pages

• [7] N. Kopteva, N. Madden, M. Stynes, Grid equidistribution for reaction-diffusion problems in one dimension, Numerical Algorithms. , 40(30) (2005), 305-322.

• [8] N. Kopteva, M. Stynes, A robust adaptive method for a quasilinear one-dimensional convection-diffusion problem, SIAM J. Numer. Anal., 39 (2001), 1446-1467.

• [9] F. Schlögl, Chemical reaction models for non-equilibrium phase transitions, Z. Physik. , 253 (1972), 147-161.

• [10] K. Fukui, The path of chemical reactions - the IRC approach, Chem. Res. , 14 (12) (1981), 363–368.

• [11] M. Goebel, U. Raitums, Optimal control of two point boundary value problems, Control and Information Sciences., 143 (1990), 281-290.

• [12] M. Popescu, Two-point boundary value problem of control systems with parameter, CCCA., 29 (2011), 1-6.

• [13] A. Omer, O. Omer, A Pray and Pretdour Model with Fuzzy Intial Values, Hacettepe Journal of Mathematics and Statistics, 41(3) (2013), 387-395.

• [14] M. S. El Naschie, From Experimental Quantum Optics to Quantum Gravity Via a Fuzzy Kahler Manifold, Chaos Solution and Fractals, 25 (2005), 969-977

• [15] M. F. Abbod, D. G. Von Keyserlingk, D. A. Linkens, M. Mahfouf, Survey of Utilization of Fuzzy Technology in Medicine and Healthcare, Fuzzy sets and system, 120 (2001), 331-349.

• [16] Barro, R. Marin, Fuzzy Logic in Medicine, Heidelberg: Physica - Verlag, (2002)

• [17] T. Allahviranloo, K. Khalilpour, A Numerical Method for Two-Point Fuzzy Boundary Value Problems, World Applied Sciences Journal , 13 (10) (2011), 2137-2147.

• [18] T. Allahviranloo, K. Khalilpour, An Initial-value Method for Two-Point Fuzzy Boundary Value Problems, World Applied Sciences Journal, 13 (10) (2011), 2148-2155

• [19] D. Dubois, H. Prade, Towards fuzzy differential calculus, Part 3: Differentiation, Fuzzy Sets and Systems, 8 (1982), 225-233.

• [20] S. Seikkala, On the Fuzzy Initial Value Problem, Fuzzy Sets and Systems, 24(3) (1987), 319–330.

• [21] M. Ghanbari, Numerical Solution of Fuzzy Initial Value Problems Under Generalization Differentiability by HPM, Int.J.Industrial Mathematics , 1(1) (2009), 19-39.

• [22] O. S. Fard, An Iterative Scheme for the Solution of Generalized System of Linear Fuzzy Differential Equations, World Applied Sciences Journal., 7 (2009), 1597-11604.

• [23] H. Saberi Najafi, F. Ramezani Sasemasi, S. Sabouri Roudkoli, S. Fazeli Nodehi, Comparison of two methods for solving fuzzy differential equations based on Euler method and Zadeh’s extension, , 2(2) (2011), 295 – 306.

• [24] L. A. Zadeh, The Concept of A linguistic Truth Variable and Its Application to Approximate Reasoning-I, II, III, Inform. Sci., 8 (1975), 199-249.

• [25] S. Sriram, P. Murugadas, On Semiring of Intuitionstic Fuzzy Matrices, Applied Mathematical Sciences, 4 (23) (2010), 1099 – 1105.

• [26] S. Siah Mansouri, N. Ahmady , Fuzzy Differential Equation by using Characterization Theorem, communication in numerical analysis, doi:10.5899/2012/cna-00054., (2012),