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.

本文提出了一种基于Haar小波的求解高阶线性和非线性边值问题的数值方案。在非线性情况下，拟线性化已被应用于处理非线性。然后，通过搭配方法计算边值问题的解，以求解计算上容易的线性方程组。所提出技术的性能在一些线性和非线性测试问题上进行了描述，包括十阶、十二阶和十三阶。通过渐近扩展研究了所提出方法的进一步收敛性。此外，计算结果已与现有结果相匹配，这表明我们的结果相对更好。