Solution of Fourth Order Singularly Perturbed Boundary Value Problem Using Septic Spline

In this paper the fourth order singularly perturbed boundary value problem is solved using septic spline. The given method is proved to be fourth order convergent. To illustrate the efficiency of the method two examples are considered. The method is also compared with the existing method and it is evident that the method is better than the existing one. MSC: 65L10

[1]  V. Shanthi,et al.  A numerical method for boundary value problems for singularly perturbed fourth-order ordinary differential equations , 2002, Appl. Math. Comput..

[2]  Relja Vulanović.  A uniform convergence result for semilinear singular perturbation problems violating the standard stability condition , 1995 .

[3]  Quintic Spline Approach to the Solution of a Singularly-Perturbed Boundary-Value Problem , 2002 .

[4]  Y. N. Reddy,et al.  Fitted fourth-order tridiagonal finite difference method for singular perturbation problems , 2007, Appl. Math. Comput..

[5]  Jalil Rashidinia,et al.  Spline approach to the solution of a singularly-perturbed boundary-value problems , 2007, Appl. Math. Comput..

[6]  Ghazala Akram,et al.  Quartic spline solution of a third order singularly perturbed boundary value problem , 2012 .

[7]  Manoj Kumar,et al.  A collection of computational techniques for solving singular boundary-value problems , 2009, Adv. Eng. Softw..

[8]  N. Ramanujam,et al.  An asymptotic finite element method for singularly perturbed third and fourth order ordinary differential equations with discontinuous source term , 2007, Appl. Math. Comput..

[9]  Vimal Singh,et al.  Perturbation methods , 1991 .

[10]  Ke Chen,et al.  Applied Mathematics and Computation , 2022 .

[11]  Y. N. Reddy,et al.  An initial-value approach for solving singularly perturbed two-point boundary value problems , 2004, Appl. Math. Comput..

[12]  I. F. Lashien,et al.  Quintic nonpolynomial spline solutions for fourth order two-point boundary value problem , 2009 .

[13]  Srinivasan Natesan,et al.  A computational method for self-adjoint singular perturbation problems using quintic spline , 2005 .

[14]  Manoj Kumar,et al.  A boundary value approach for a class of linear singularly perturbed boundary value problems , 2009, Adv. Eng. Softw..

[15]  Jesús Vigo-Aguiar,et al.  An efficient numerical method for singular perturbation problems , 2006 .

[16]  N. Ramanujam,et al.  A boundary value technique for boundary value problems for singularly perturbed fourth-order ordinary differential equations , 2004 .

[17]  Arshad Khan,et al.  Sextic spline solution of a singularly perturbed boundary-value problems , 2006, Appl. Math. Comput..