SIAM Journal on Scientific Computing
On Krylov Subspace Approximations to the Matrix Exponential Operator
SIAM Journal on Numerical Analysis
A new class of time discretization schemes for the solution of nonlinear PDEs
Journal of Computational Physics
Computation of Gauss-Kronrod of quadrature rules
Mathematics of Computation
Deferred Correction Methods for Initial Boundary Value Problems
Journal of Scientific Computing
Adaptive solution of partial differential equations in multiwavelet bases
Journal of Computational Physics
Krylov subspace methods for variable-coefficient initial-boundary value problems
Krylov subspace methods for variable-coefficient initial-boundary value problems
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Krylov subspace spectral methods have been shown to be high-order accurate in time and more stable than explicit time-stepping methods, but also more difficult to implement efficiently. This paper describes how these methods can be fashioned into practical solvers by exploiting the simple structure of differential operators Numerical results concerning accuracy and efficiency are presented for parabolic problems in one and two space dimensions.