How to cite this paper
Sabir, Z & Raja, M. (2014). Numeric treatment of nonlinear second order multi-point boundary value problems using ANN, GAs and sequential quadratic programming technique.International Journal of Industrial Engineering Computations , 5(3), 431-442.
Refrences
Cannon, J. R. (1984). The one-dimensional heat equation, volume 23 of Encyclopedia of Mathematics and its Applications.
Cannon, J. R., Esteva, S. P., & Van Der Hoek, J. (1987). A Galerkin procedure for the diffusion equation subject to the specification of mass. SIAM Journal on Numerical Analysis, 24(3), 499-515.
Deimling, K. (1985). Nonlinear Functional Analysis. Springler-Verlag, Berlin.
Das, S., Kumar, S., & Singh, O. P. (2010). Solutions of Nonlinear Second Order Multi-point Boundary Value Problems by Homotopy Perturbation Method. Applied Mathematics: An International Journal, 5(10), 1592-1600.
Erbe, L. H., & Wang, H. (1994). On the existence of positive solutions of ordinary differential equations. Proceedings of the American Mathematical Society, 120(3), 743-748.
Gupta, C. P. (1992). Solvability of a three-point nonlinear boundary value problem for a second order ordinary differential equation. Journal of Mathematical Analysis and Applications, 168(2), 540-551.
Gupta, C. P. (1994). A note on a second order three-point boundary value problem. Journal of Mathematical Analysis and Applications, 186(1), 277-281.
Gupta, C. P., & Trofimchuk, S. I. (1997). A sharper condition for the solvability of a three-point second order boundary value problem. Journal of Mathematical Analysis and Applications, 205(2), 586-597.
Guo, D., & Lakshmikantham, V. (1988). Nonlinear Problems in Abstract Cones (Vol. 5). San Diego: Academic press.
Eloe, P. W., & Henderson, J. (1994). Multipoint boundary value problems for ordinary differential systems. Journal of Differential Equations, 114(1), 232-242.
Ilin, V. A., & Moiseev, E. I. (1987). Nonlocal boundary-value problem of the first kind for a Sturm-Liouville operator in its differential and finite difference aspects. Differential Equations, 23(7), 803-810.
Khan, J. A., Zahoor, R. M. A., & Qureshi, I. M. (2009, December). Swarm intelligence for the solution of problems in differential equations. In Environmental and Computer Science, 2009. ICECS & apos; 09. Second International Conference on (pp. 141-147). IEEE.
Khan, A., Raja, M. A. Z., & Ijaz Mansoor Qureshi, J. (2012). An application of evolutionary computational technique to non-linear singular system arising in polytrophic and isothermal sphere. Global Journal of Researches In Engineering, 12(1-I).
Krasnosel & apos; skij, M. A. (1964). Positive solutions of operator equations (p. 381). L. F. Boron (Ed.). Groningen: P. Noordhoff.
Liu, B. (2002). Positive solutions of a nonlinear three-point boundary value problem. Computers & Mathematics with Applications, 44(1), 201-211.
Ma, R. (1999). Positive solutions of a nonlinear three-point boundary-value problem. Electronic Journal of Differential Equations, 1999(34), 1-8.
Ma, R. (2001). Positive solutions for second-order three-point boundary value problems. Applied Mathematics Letters, 14(1), 1-5.
Raja, M. A. Z., & Samar, R. (2012). Neural network optimized with evolutionary computing technique for solving the 2-dimensional Bratu problem. Neural Computing and Applications, 1-12.
Timoshenko, S. P., & Gere, J. M. (1961). Theory of elastic stability. 1961.
Webb, J. R. L. (2001). Positive solutions of some three point boundary value problems via fixed point index theory. Nonlinear Analysis: Theory, Methods & Applications, 47(7), 4319-4332.
Cannon, J. R., Esteva, S. P., & Van Der Hoek, J. (1987). A Galerkin procedure for the diffusion equation subject to the specification of mass. SIAM Journal on Numerical Analysis, 24(3), 499-515.
Deimling, K. (1985). Nonlinear Functional Analysis. Springler-Verlag, Berlin.
Das, S., Kumar, S., & Singh, O. P. (2010). Solutions of Nonlinear Second Order Multi-point Boundary Value Problems by Homotopy Perturbation Method. Applied Mathematics: An International Journal, 5(10), 1592-1600.
Erbe, L. H., & Wang, H. (1994). On the existence of positive solutions of ordinary differential equations. Proceedings of the American Mathematical Society, 120(3), 743-748.
Gupta, C. P. (1992). Solvability of a three-point nonlinear boundary value problem for a second order ordinary differential equation. Journal of Mathematical Analysis and Applications, 168(2), 540-551.
Gupta, C. P. (1994). A note on a second order three-point boundary value problem. Journal of Mathematical Analysis and Applications, 186(1), 277-281.
Gupta, C. P., & Trofimchuk, S. I. (1997). A sharper condition for the solvability of a three-point second order boundary value problem. Journal of Mathematical Analysis and Applications, 205(2), 586-597.
Guo, D., & Lakshmikantham, V. (1988). Nonlinear Problems in Abstract Cones (Vol. 5). San Diego: Academic press.
Eloe, P. W., & Henderson, J. (1994). Multipoint boundary value problems for ordinary differential systems. Journal of Differential Equations, 114(1), 232-242.
Ilin, V. A., & Moiseev, E. I. (1987). Nonlocal boundary-value problem of the first kind for a Sturm-Liouville operator in its differential and finite difference aspects. Differential Equations, 23(7), 803-810.
Khan, J. A., Zahoor, R. M. A., & Qureshi, I. M. (2009, December). Swarm intelligence for the solution of problems in differential equations. In Environmental and Computer Science, 2009. ICECS & apos; 09. Second International Conference on (pp. 141-147). IEEE.
Khan, A., Raja, M. A. Z., & Ijaz Mansoor Qureshi, J. (2012). An application of evolutionary computational technique to non-linear singular system arising in polytrophic and isothermal sphere. Global Journal of Researches In Engineering, 12(1-I).
Krasnosel & apos; skij, M. A. (1964). Positive solutions of operator equations (p. 381). L. F. Boron (Ed.). Groningen: P. Noordhoff.
Liu, B. (2002). Positive solutions of a nonlinear three-point boundary value problem. Computers & Mathematics with Applications, 44(1), 201-211.
Ma, R. (1999). Positive solutions of a nonlinear three-point boundary-value problem. Electronic Journal of Differential Equations, 1999(34), 1-8.
Ma, R. (2001). Positive solutions for second-order three-point boundary value problems. Applied Mathematics Letters, 14(1), 1-5.
Raja, M. A. Z., & Samar, R. (2012). Neural network optimized with evolutionary computing technique for solving the 2-dimensional Bratu problem. Neural Computing and Applications, 1-12.
Timoshenko, S. P., & Gere, J. M. (1961). Theory of elastic stability. 1961.
Webb, J. R. L. (2001). Positive solutions of some three point boundary value problems via fixed point index theory. Nonlinear Analysis: Theory, Methods & Applications, 47(7), 4319-4332.