Uniformly high order accurate essentially non-oscillatory schemes, 111
Journal of Computational Physics
Efficient implementation of essentially non-oscillatory shock-capturing schemes
Journal of Computational Physics
Finite difference schemes and partial differential equations
Finite difference schemes and partial differential equations
SIAM Journal on Numerical Analysis
Adaptive multiresolution schemes for shock computations
Journal of Computational Physics
Journal of Computational Physics
Application of generalized wavelets: an adaptive multiresolution scheme
Journal of Computational and Applied Mathematics
Total variation diminishing Runge-Kutta schemes
Mathematics of Computation
Journal of Computational Physics
A Wavelet-Optimized, Very High Order Adaptive Grid and Order Numerical Method
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
Solving Hyperbolic PDEs Using Interpolating Wavelets
SIAM Journal on Scientific Computing
Point Value Multiscale Algorithms for 2D Compressible Flows
SIAM Journal on Scientific Computing
ON THE WAVELET OPTIMIZED FINITE DIFFERENCE METHOD
ON THE WAVELET OPTIMIZED FINITE DIFFERENCE METHOD
A conservative fully adaptive multiresolution algorithm for parabolic PDEs
Journal of Computational Physics
Adaptive wavelet representation and differentiation on block-structured grids
Applied Numerical Mathematics - Special issue on applied and computational mathematics: Selected papers of the fourth PanAmerican workshop
Interpolation and Approximation of Piecewise Smooth Functions
SIAM Journal on Numerical Analysis
An Adaptive Wavelet Collocation Method for Fluid-Structure Interaction at High Reynolds Numbers
SIAM Journal on Scientific Computing
A second order primitive preconditioner for solving all speed multi-phase flows
Journal of Computational Physics
Adaptive multiresolution WENO schemes for multi-species kinematic flow models
Journal of Computational Physics
IEEE Transactions on Image Processing
Applied Numerical Mathematics
On (essentially) non-oscillatory discretizations of evolutionary convection-diffusion equations
Journal of Computational Physics
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In this work an efficient third order non-linear finite difference scheme for solving adaptively hyperbolic systems of one-dimensional conservation laws is developed. The method is based on applying to the solution of the differential equation an interpolating wavelet transform at each time step, generating a multilevel representation for the solution, which is thresholded and a sparse point representation is generated. The numerical fluxes obtained by a Lax-Friedrichs flux splitting are evaluated on the sparse grid by an essentially non-oscillatory (ENO) approximation, which chooses the locally smoothest stencil among all the possibilities for each point of the sparse grid. The time evolution of the differential operator is done on this sparse representation by a total variation diminishing (TVD) Runge-Kutta method. Four classical examples of initial value problems for the Euler equations of gas dynamics are accurately solved and their sparse solutions are analyzed with respect to the threshold parameters, confirming the efficiency of the wavelet transform as an adaptive grid generation technique.