Sextic spline solutions of fifth order boundary value problems

An Enhanced Quartic B-spline Method for a Class of Non-linear Fifth-Order Boundary Value Problems

“…Example (4.1) has been solved by the sextic spline method (SSM) in [5][6][7][8], non-polynomial sextic spline method (NSSM) in [9][10][11][12], cubic spline method (CSM) in [13], quartic spline method (QSM) in [14][15][16], and finite-difference method (FDM) in [27]. We collect their respective maximum absolute errors in Table 3.…”

“…Besides, we also compare our MAE[y (k) (x, n)] (k = 1, 2, 3, 4, n = 10, 20, 40) with that of the methods in [7,13,16]. The other methods have not provided numerical derivatives of (4.1).…”

“…Among these methods, sextic (polynomial and non-polynomial) splines have been extensively used. In fact, the methods in [4][5][6][7][8] are based on sextic polynomial splines. However, the methods are only second-order convergent with O(h 2 ) errors.…”

B-Spline Collocation Method for Solving Singularly Perturbed Boundary Value Problems

“…Up to now, B-spline approximation method for numerical solutions has been researched by various researchers [6]- [8].…”

An Effective Method for Seventh-Order Boundary Value Problems

“…For instance, Caglar et al [1] as well as Siddiqi and Ghazala [2] and Jalil et al [3] have applied spline functions, the finite difference method by Khan [4], the Adomian Decomposition Method was used by Wazwaz [5], Aslam and Tauseef [6] considered an Iteration Method based on decomposition procedure for the solution of fifth order boundary value problem while Shaowei [7] used Homotopy Perturbation Method. Siddiqi et al [8] utilized Variational Iteration Method (VIM) for approximate solution of seventh-order boundary value problem.…”