Wavelet Galerkin method for fourth order linear and nonlinear differential equations

In this paper, we propose a wavelet Galerkin method for fourth order linear and nonlinear differential equations using compactly supported Daubechies wavelets. 2-term connection coefficients have been effectively used for a computationally economical evaluation of higher order derivatives. The orthogonality and compact support properties of basis functions lead to highly sparse linear systems. The quasilinearization strategy is effectively employed in dealing with wavelet coefficients of nonlinear problems. The stability and the convergence analysis, in the form of error analysis, have been carried out. An efficient compression algorithm is proposed to reduce the computational cost of the method. Finally, the method is tested on several examples and found to be in good agreement with exact solution.