High Order Schemes for Resolving Waves: Number of Points per Wavelength
Journal of Scientific Computing
Adaptive High-Order Finite-Difference Method for Nonlinear Wave Problems
Journal of Scientific Computing
Journal of Scientific Computing
Adaptive radial basis function methods for time dependent partial differential equations
Applied Numerical Mathematics
An adaptive multilevel wavelet collocation method for elliptic problems
Journal of Computational Physics
Numerical solution of differential equations using Haar wavelets
Mathematics and Computers in Simulation
Simultaneous space-time adaptive wavelet solution of nonlinear parabolic differential equations
Journal of Computational Physics
Journal of Computational Physics
Adaptive multiresolution WENO schemes for multi-species kinematic flow models
Journal of Computational Physics
Journal of Computational and Applied Mathematics
ENO adaptive method for solving one-dimensional conservation laws
Applied Numerical Mathematics
Adaptive radial basis function methods for time dependent partial differential equations
Applied Numerical Mathematics
Simulating 2D Waves Propagation in Elastic Solid Media Using Wavelet Based Adaptive Method
Journal of Scientific Computing
Journal of Computational Electronics
Adaptive wavelet collocation methods for image segmentation using TV---Allen---Cahn type models
Advances in Computational Mathematics
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Wavelets detect information at different scales and at different locations throughout a computational domain. Furthermore, wavelets can detect the local polynomial content of computational data. Numerical methods are most efficient when the basis functions of the method are similar to the data present. By designing a numerical scheme in a completely adaptive manner around the data present in a computational domain, one can obtain optimal computational efficiency. This paper extends the numerical wavelet-optimized finite difference (WOFD) method to arbitrarily high order, so that one obtains, in effect, an adaptive grid and adaptive order numerical method which can achieve errors equivalent to errors obtained with a "spectrally accurate" numerical method.