Abstract
Multilevel augmentation method with wavelet bases is demonstrated to show as the fast technique for solving singularly perturbed problems. Linear and quadratic wavelet bases are employed for constructing the full form of matrix system. To reduce the size of matrix coefficients, the multilevel augmented technique is applied at each current basis level. It is found that the multilevel augmentation method is faster than the standard multilevel method at the same order of accuracy. Convergent rates for linear and quadratic bases are 2 and 4 respectively. By the application of wavelet bases, numerical accuracy can be easily improved by increasing just desired levels in the multilevel augmentation process.
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