A MULTIRESOLUTION ADAPTIVE WAVELET METHOD FOR NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS

The multiscale complexity of modern problems in computational science and engineering can prohibit the use traditional numerical methods multi-dimensional simulations. Therefore, novel algorithms are required these situations to solve partial differential equations (PDEs) with features evolving on a wide range spatial temporal scales. To meet challenges, we present multiresolution wavelet algorithm PDEs significant data compression explicit error control. We discretize space by projecting fields derivative operators onto basis functions. provide estimates for representation their derivatives. Then, our used construct sparse discretization which guarantees prescribed accuracy. Additionally, embed predictor-corrector procedure within integration dynamically adapt grid maintain accuracy solution PDE as it evolves. examples highlight adaptivity approach.