Ten lectures on wavelets
On the representation of operators in bases of compactly supported wavelets
SIAM Journal on Numerical Analysis
A class of bases in L2 for the sparse representations of integral operators
SIAM Journal on Mathematical Analysis
Wavelet-like bases for the fast solutions of second-kind integral equations
SIAM Journal on Scientific Computing
The spectral element method for the shallow water equations on the sphere
Journal of Computational Physics
On the adaptive numerical solution of nonlinear partial differential equations in wavelet bases
Journal of Computational Physics
The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
SIAM Journal on Numerical Analysis
A new class of time discretization schemes for the solution of nonlinear PDEs
Journal of Computational Physics
A Multiresolution Approach to Regularization of Singular Operators and Fast Summation
SIAM Journal on Scientific Computing
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Singular operators in multiwavelet bases
IBM Journal of Research and Development
Multi-resolution analysis of wiener-type uncertainty propagation schemes
Journal of Computational Physics
Rooted tree analysis of Runge-Kutta methods with exact treatment of linear terms
Journal of Computational and Applied Mathematics
Fast iterative solution of elliptic control problems in wavelet discretization
Journal of Computational and Applied Mathematics
Practical Implementation of Krylov Subspace Spectral Methods
Journal of Scientific Computing
Extended Legendre Wavelets Neural Network
ICIC '08 Proceedings of the 4th international conference on Intelligent Computing: Advanced Intelligent Computing Theories and Applications - with Aspects of Artificial Intelligence
Time Acceleration Methods for Advection on the Cubed Sphere
ICCS 2009 Proceedings of the 9th International Conference on Computational Science
Rooted tree analysis of Runge-Kutta methods with exact treatment of linear terms
Journal of Computational and Applied Mathematics
Multiresolution quantum chemistry in multiwavelet bases
ICCS'03 Proceedings of the 2003 international conference on Computational science
Techniques for solving integral and differential equations by Legendre wavelets
International Journal of Systems Science
Fast transform from an adaptive multi-wavelet representation to a partial Fourier representation
Journal of Computational Physics
Numerical solution of telegraph equation using interpolating scaling functions
Computers & Mathematics with Applications
Journal of Computational and Applied Mathematics
Adaptive discontinuous Galerkin methods in multiwavelets bases
Applied Numerical Mathematics
The EPS method: A new method for constructing pseudospectral derivative operators
Journal of Computational Physics
Convergence and condition number of multi-projection operators by Legendre wavelets
Computers & Mathematics with Applications
Stable and Spectrally Accurate Schemes for the Navier-Stokes Equations
SIAM Journal on Scientific Computing
Adaptive wavelet collocation methods for image segmentation using TV---Allen---Cahn type models
Advances in Computational Mathematics
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We construct multiresolution representations of derivative and exponential operators with linear boundary conditions in multiwavelet bases and use them to develop a simple, adaptive scheme for the solution of nonlinear, time-dependent partial differential equations. The emphasis on hierarchical representations of functions on intervals helps to address issues of both high-order approximation and efficient application of integral operators, and the lack of regularity of multiwavelets does not preclude their use in representing differential operators. Comparisons with finite difference, finite element, and spectral element methods are presented, as are numerical examples with the heat equation and Burgers' equation.