Sextic spline solution of fifth-order boundary value problems

Numerical Solution of Fifth Order Boundary Value Problems by Petrov-Galerkin Method with Quartic B-Splines as Basis Functions and Quintic B-Splines as Weight Functions

“…Syam and Ahili [10] presented combination of Adomain decomposition method and the Homotopy method to solve a fifth order singularly perturbed boundary value problem arising in viscoelastic flows. Zhao [11] developed the solution of fifth order boundary value problems by variational iteration method, Lamnii et al [12] developed the sextic spline collocation method to solve special case of fifth order boundary value problems. Kasi Viswanadham and Sreenivasulu [13] developed the quartic B-spline Galerkin method to a general fifth order boundary value problem.…”

Discrete septic spline quasi-interpolants for solving generalized Fredholm integral equation of the second kind via three degenerate kernel methods

“…The result of their work is twofold: on the one hand, they achieve an approximation order 0ðh 5 Þ for the left method, on the other hand, they achieve another approximation of the order of 0ðh 6 Þ for the right method. Recently, a paper reached the sextic spline, working on two collocation methods, using both, spline interpolants and spline quasi-interpolants to solve the fifthorder boundary value problems (see [22]). …”

Numerical Solution of Fifth Order Boundary Value Problems by Petrov-Galerkin Method with Quintic B-splines as basis functions and Septic B-Splines as weight functions

“…Over the years, many researchers have worked on boundary value problems by using different methods for numerical solutions [4][5][6][7][8][9][10][11][12][13]. Wazwaz [4] developed the solution of special type of fifth order boundary value problems by using the modified Adomain decomposition method and he provided the solution in the form of a rapidly convergent series, Siddiqi et al [5] presented the solution of a special case of linear fifth order boundary value problems by using quartic spline functions, Rashidinia et al [6] presented the solution of a special case of linear fifth order boundary value problem by using non-polynomial spline functions techniques, Noor and Sayed [7] applied the Homotopy perturbation method for solving fifth order boundary value problems, Caglar and Caglar [8] presented the Local polynomial regression method to solve the special case of fifth order boundary value problems, Gamel [9] presented the solution of fifth order boundary value problems by SincGalerkin method, Syam and Ahili [10] presented combination of Adomain decomposition method and the Homotopy method to solve a fifth order singularly perturbed boundary value problem arising in viscoelastic flows, Zhao [11] developed the solution of fifth order boundary value problems by variational iteration method, Lamnii et al [12] developed the sextic spline collocation method to solve special case of fifth order boundary value problems, Kasi Viswanadham and Sreenivasulu [13] developed the quartic B-spline Galerkin method to a general solve fifth order boundary value problem. So far, fifth order boundary value problems have not been solved by using Petrov-Galerkin method with quintic B-splines as basis functions and septic B-splines as weight functions .…”