Liu, Xioajing; Zhou, Youhe; Wang, Xiaomin; Wang, Jizeng A wavelet method for solving a class of nonlinear boundary value problems. (English) Zbl 1277.65058 Commun. Nonlinear Sci. Numer. Simul. 18, No. 8, 1939-1948 (2013). Summary: We develop an approximation scheme for a function defined on a bounded interval by combining techniques of boundary extension and Coiflet-type wavelet expansion. Such a modified wavelet approximation allows each expansion coefficient being explicitly expressed by a single-point sampling of the function, and allows boundary values and derivatives of the bounded function to be embedded in the modified wavelet basis. By incorporating this approximation scheme into the conventional Galerkin method, the interpolating property makes the solution of boundary value problems with strong nonlinearity very effective and accurate. As an example, we apply the proposed method to the solution of the Bratu-type equations. Results demonstrate a much better accuracy than most methods developed so far. Interestingly, unlike most existing methods, numerical errors of the present solutions are not sensitive to the nonlinear intensity of the equations. Cited in 38 Documents MSC: 65L10 Numerical solution of boundary value problems involving ordinary differential equations 34B15 Nonlinear boundary value problems for ordinary differential equations 65T60 Numerical methods for wavelets Keywords:modified wavelet Galerkin method; strong nonlinearity; boundary value problems; Bratu equation; numerical examples; Coiflet-type wavelet expansion PDFBibTeX XMLCite \textit{X. Liu} et al., Commun. Nonlinear Sci. Numer. Simul. 18, No. 8, 1939--1948 (2013; Zbl 1277.65058) Full Text: DOI Link