Split-step methods for the solution of the nonlinear Schro¨dinger equation
SIAM Journal on Numerical Analysis
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
On symmetric schemes and differential-algebraic equations
SIAM Journal on Scientific and Statistical Computing
Pseudospectra of Linear Operators
SIAM Review
The Midpoint Scheme and Variants for Hamiltonian Systems: Advantages and Pitfalls
SIAM Journal on Scientific Computing
Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations
Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations
A New Class of Optimal High-Order Strong-Stability-Preserving Time Discretization Methods
SIAM Journal on Numerical Analysis
On Strong Stability Preserving Time Discretization Methods
Journal of Scientific Computing
Finite Differences And Partial Differential Equations
Finite Differences And Partial Differential Equations
On Symplectic and Multisymplectic Schemes for the KdV Equation
Journal of Scientific Computing
Linear Instability of the Fifth-Order WENO Method
SIAM Journal on Numerical Analysis
Numerical Methods for Evolutionary Differential Equations
Numerical Methods for Evolutionary Differential Equations
Highly Efficient Strong Stability-Preserving Runge-Kutta Methods with Low-Storage Implementations
SIAM Journal on Scientific Computing
High Order Strong Stability Preserving Time Discretizations
Journal of Scientific Computing
Splitting Integrators for Nonlinear Schrödinger Equations Over Long Times
Foundations of Computational Mathematics
On the Linear Stability of the Fifth-Order WENO Discretization
Journal of Scientific Computing
| Hi-index | 0.00 |
In the course of simulation of differential equations, especially of marginally stable differential problems using marginally stable numerical methods, one occasionally comes across a correct computation that yields surprising, or unexpected results. We examine several instances of such computations. These include (i) solving Hamiltonian ODE systems using almost conservative explicit Runge-Kutta methods, (ii) applying splitting methods for the nonlinear Schrodinger equation, and (iii) applying strong stability preserving Runge-Kutta methods in conjunction with weighted essentially non-oscillatory semi-discretizations for nonlinear conservation laws with discontinuous solutions. For each problem and method class we present a simple numerical example that yields results that in our experience many active researchers are finding unexpected and unintuitive. Each numerical example is then followed by an explanation and a resolution of the practical problem.