Non-polynomial spline solution of singularly perturbed boundary-value problems

Quartic spline solution of a third order singularly perturbed boundary value problem

“…A numerical method for a class of second order singularly perturbed two point boundary value problems on a uniform mesh using a compressed spline was proposed by Mohanty and Jha [8]. Quartic non-polynomial spline functions were used to develop a class of numerical methods for solving self adjoint second order singularly perturbed two point boundary value problems by Tirmizi et al [13]. Difference schemes were developed for the numerical solution of second order two point singularly perturbed boundary value problems using a tension spline by Kadalbajoo and Patidar [4].…”

A new algorithm based on spline in tension approximation for 1D quasi-linear parabolic equations on a variable mesh

“…They [17] constructed adaptive spline function to solve initial and boundary value problems of ordinary and partial differential equations, which, when applied to the test models produced oscillation free solutions. Various numerical methods based on polynomial and non-polynomial spline approximations have been developed to obtain the solution of ordinary and partial differential equations [1][2][3][5][6][7][8]11,12,[16][17][18][19][20][21][22][23][24][26][27][28][29]30,[32][33][34][35][36][37]40,41]. Mohanty [25] developed a variable mesh method of Numerov type for the solution of nonlinear two-point boundary value problems.…”

Numerical Solution of Singularly Perturbed Boundary Value Problems Based on Optimal Control Strategy

“…There are many known methods for solving problems in the form of (1) and (2), such as collocation methods [2][3][4], finite difference methods [11], finite element methods [7,9,18,25,26], boundary value techniques [1,5,22], spline methods [10,15,20,21,24,27], and so on. In recent years, a large number of special purpose methods have been developed to provide accurate numerical solutions.…”