References
- S. Bellew and E. O'Riordan. A parameter robust numerical method for a system of two singularly perturbed convection-diffusion equations. Applied Numerical Mathematics, 51(23):171–186, 2004. http://dx.doi.org/10.1016/j.apnum.2004.05.006. doi: 10.1016/j.apnum.2004.05.006
- G.F. Carey and H.T. Dinh. Grading functions and mesh redistribution. SIAM Journal of Numerical Analysis, 22(5):1028–1040, 1985. http://dx.doi.org/10.1137/0722061. doi: 10.1137/0722061
- X. Cheng and C. Zhong. Existence of positive solutions for a second-order ordinary differential system. J. Math. Anal. Appl., 312(1):14–23, 2005. http://dx.doi.org/10.1016/j.jmaa.2005.03.016.
- C.C. Christara and K.S. Ng. Adaptive techniques for spline collocation. Computing, 76(3-4):259–277, 2006. http://dx.doi.org/10.1007/s00607-005-0141-3. doi: 10.1007/s00607-005-0141-3
- C.C. Christara and K.S. Ng. Optimal quadratic and cubic spline collocation on nonuniform partitions. Computing, 76(3-4):227–257, 2006. http://dx.doi.org/10.1007/s00607-005-0140-4.
- E.Y. Deeba and S.A. Khuri. Nonlinear equations, pp. 562–570. Taylor & Francis., 1999. http://dx.doi.org/10.1002/047134608X.W2441.
- M. Dehghan and A. Saadatmandi. The numerical solution of a nonlinear system of second-order boundary value problems using sinc-collocation method. Math. Comput. Modelling, 46(1112):1434–1441, 2007. http://dx.doi.org/10.1016/j.mcm.2007.02.002. doi: 10.1016/j.mcm.2007.02.002
- F. Geng and M. Cui. Solving a nonlinear system of second order boundary value problems. J. Math. Anal. Appl., 327(2):1167–1181, 2007. http://dx.doi.org/10.1016/j.jmaa.2006.05.011. doi: 10.1016/j.jmaa.2006.05.011
- S.A. Khuri and A. Sayfy. Spline collocation approach for the numerical solution of generalized system of second-order boundary-valued problem. Applied Mathematical Sciences J., 3(45):2227–2239, 2009.
- S.A. Khuri and A. Sayfy. A spline collocation approach for the numerical solution of a generalized nonlinear Klein-Gordon equation. Applied Mathematics and Computation, 216(4):1047–1056, 2010. http://dx.doi.org/10.1016/j.amc.2010.01.122. doi: 10.1016/j.amc.2010.01.122
- S.A. Khuri and A. Sayfy. Troesch's problem: A B-spline collocation approach. Mathematical and Computer Modelling, 54(910):1907–1918, 2011. http://dx.doi.org/10.1016/j.mcm.2011.04.030. doi: 10.1016/j.mcm.2011.04.030
- S.A. Khuri and A. Sayfy. The boundary layer problem: A fourth-order collocation approach. Computers and Mathematics with Applications, 64(6):2089–2099, 2012. http://dx.doi.org/10.1016/j.camwa.2012.04.005. doi: 10.1016/j.camwa.2012.04.005
- S.A. Khuri and A. Sayfy. A spline collocation approach for a generalized parabolic problem subject to non-classical conditions. Applied Mathematics and Computation, 218(18):9187–9196, 2012. http://dx.doi.org/10.1016/j.amc.2012.02.075. doi: 10.1016/j.amc.2012.02.075
- F. Lang and X. Xu. Quintic B-spline collocation method for second order mixed boundary value problem. Computer Physics Communications, 183(4):913–921, 2012. http://dx.doi.org/10.1016/j.cpc.2011.12.017. doi: 10.1016/j.cpc.2011.12.017
- J. Lu. Variational iteration method for solving a nonlinear system of second-order boundary value problems. Comput. Math. Appl., 54(78):1133–1138, 2007. http://dx.doi.org/10.1016/j.camwa.2006.12.060.
- S. Matthews, E. O'Riordan and G.I. Shishkin. A numerical method for system of singularly perturbed reaction-diffusion equations. J. Comp. Appl. Math., 145(1):151–166, 2002. http://dx.doi.org/10.1016/S0377-0427(01)00541-6. doi: 10.1016/S0377-0427(01)00541-6
- A. Saadatmandi, M. Dehghan and A. Eftekhari. Application of He's homotopy perturbation method for non-linear system of second-order boundary value problems. Nonlinear Analysis: Real World Applications, 10(3):1912–1922, 2009. http://dx.doi.org/10.1016/j.nonrwa.2008.02.032. doi: 10.1016/j.nonrwa.2008.02.032
- A. Saadatmandi and J.A. Farsangi. Chebychev finite difference method for a nonlinear system of second-order boundary value problems. Appl. Math. Comput., 192(2):586–591, 2007. http://dx.doi.org/10.1016/j.amc.2007.02.148.
- A. Tamilselvan, N. Ramanujam and V. Shanthi. A numerical method for singularly perturbed weakly coupled system of two second order ordinary differential equations with discontinuous source term. Journal of Computational and Applied Mathematics, 202(2):203–216, 2007. http://dx.doi.org/10.1016/j.cam.2006.02.025. doi: 10.1016/j.cam.2006.02.025
- T. Valanarasu and N. Ramanujam. An asymptotic initial value method for boundary value problems for a system of singularly perturbed second order ordinary differential equations. Applied Mathematics and Computation, 147(1):227–240, 2004. http://dx.doi.org/10.1016/S0096-3003(02)00663-X. doi: 10.1016/S0096-3003(02)00663-X