Topics in matrix analysis
Numerical recipes in C: the art of scientific computing
Numerical recipes in C: the art of scientific computing
Numerical methods and software
Numerical methods and software
Non-oscillatory central differencing for hyperbolic conservation laws
Journal of Computational Physics
SIAM Journal on Scientific Computing
Numerical methods for hyperbolic conservation laws with stiff relaxation I: spurious solutions
SIAM Journal on Applied Mathematics
Runge-Kutta methods for hyperbolic conservation laws with stiff relaxation terms
Journal of Computational Physics
Uniformly Accurate Schemes for Hyperbolic Systems with Relaxation
SIAM Journal on Numerical Analysis
SIAM Journal on Numerical Analysis
Journal of Computational Physics
Numerical Schemes for Hyperbolic Systems of Conservation Laws with Stiff Diffusive Relaxation
SIAM Journal on Numerical Analysis
MOL solvers for hyperbolic PDEs with source terms
Mathematics and Computers in Simulation - IMACS sponsored special issue on method of lines
Computer-Aided Analysis of Difference Schemes for Partial Differential Equations
Computer-Aided Analysis of Difference Schemes for Partial Differential Equations
Numerical Solutions for Partial Differential Equations: Problem Solving Using Mathematica (with Disk)
Runge--Kutta Solutions of a Hyperbolic Conservation Law with Source Term
SIAM Journal on Scientific Computing
A Third-Order Semidiscrete Central Scheme for Conservation Laws and Convection-Diffusion Equations
SIAM Journal on Scientific Computing
Central Differencing Based Numerical Schemes for Hyperbolic Conservation Laws with Relaxation Terms
SIAM Journal on Numerical Analysis
Uniformly Accurate Diffusive Relaxation Schemes for Multiscale Transport Equations
SIAM Journal on Numerical Analysis
Discretization of Unsteady Hyperbolic Conservation Laws
SIAM Journal on Numerical Analysis
On Discrete Maximum Principles for Linear Equation Systems and Monotonicity of Difference Schemes
SIAM Journal on Matrix Analysis and Applications
On Monotonicity of Difference Schemes for Computational Physics
SIAM Journal on Scientific Computing
Central Runge--Kutta Schemes for Conservation Laws
SIAM Journal on Scientific Computing
Fourth-Order Nonoscillatory Upwind and Central Schemes for Hyperbolic Conservation Laws
SIAM Journal on Numerical Analysis
Implicit---Explicit Runge---Kutta Schemes and Applications to Hyperbolic Systems with Relaxation
Journal of Scientific Computing
Capturing shock waves in inelastic granular gases
Journal of Computational Physics
On Stability, Monotonicity, and Construction of Difference Schemes I: Theory
SIAM Journal on Scientific Computing
On Stability, Monotonicity, and Construction of Difference Schemes II: Applications
SIAM Journal on Scientific Computing
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The stability of nonlinear explicit difference schemes with not, in general, open domains of the scheme operators are studied. For the case of path-connected, bounded, and Lipschitz domains, we establish the notion that a multi-level nonlinear explicit scheme is stable iff (if and only if) the corresponding scheme in variations is stable. A new modification of the central Lax-Friedrichs (LxF) scheme is developed to be of the second-order accuracy. The modified scheme is based on nonstaggered grids. A monotone piecewise cubic interpolation is used in the central scheme to give an accurate approximation for the model in question. The stability of the modified scheme is investigated. Some versions of the modified scheme are tested on several conservation laws, and the scheme is found to be accurate and robust. As applied to hyperbolic conservation laws with, in general, stiff source terms, it is constructed a second-order nonstaggered central scheme based on operator-splitting techniques.