Abstract
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 to be very effective and accurate. As an example, we have applied 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.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Communications in Nonlinear Science and Numerical Simulation
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
