Abstract
This paper presents a numerical scheme based on Haar wavelet for the solutions of higher order linear and nonlinear boundary value problems. In nonlinear cases, quasilinearization has been applied to deal with nonlinearity. Then, through collocation approach computing solutions of boundary value problems reduces to solve a system of linear equations which are computationally easy. The performance of the proposed technique is portrayed on some linear and nonlinear test problems including tenth, twelfth, and thirteen orders. Further convergence of the proposed method is investigated via asymptotic expansion. Moreover, computed results have been matched with the existing results, which shows that our results are comparably better. It is observed from convergence theoretically and verified computationally that by increasing the resolution level the accuracy also increases.
Highlights
Higher-order boundary value problems (HOBVPs) have widespread applications in diverse areas of science and engineering
If an infinite smooth sheet of fluid is heated from below in the presence of a magnetic field in gravity direction, instability occurs. When this instability is ordinary convection, it is modeled through tenth order boundary value problems (BVPs)
If instability sets are as over stability, it is modeled by twelfth order boundary value problem [3]
Summary
Higher-order boundary value problems (HOBVPs) have widespread applications in diverse areas of science and engineering. If an infinite smooth sheet of fluid is heated from below in the presence of a magnetic field in gravity direction, instability occurs When this instability is ordinary convection, it is modeled through tenth order boundary value problems (BVPs). Arifeen et al Advances in Difference Equations (2021) 2021:347 homotopy analysis method and nonpolynomial splines technique for solving ninth order BVPs. Siddiqi et al [11, 12] used spline technique for solving linear tenth and twelfth order BVPs. For the past few decades, wavelet based numerical methods have gained great importance for solution of HOBVPs, because of their ease in implementation. This approach became popular and has been applied to different problems In this direction, Lepik [17] presented the solution of a higher order differential equation by using HW. Convergence result will be a part of this work
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