Uniformly high order accurate essentially non-oscillatory schemes, 111
Journal of Computational Physics
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
Runge-Kutta methods for hyperbolic conservation laws with stiff relaxation terms
Journal of Computational Physics
Numerical schemes 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
Journal of Computational Physics
Numerical Schemes for Hyperbolic Systems of Conservation Laws with Stiff Diffusive Relaxation
SIAM Journal on Numerical Analysis
Stability of Finite and Infinite Dimensional Systems
Stability of Finite and Infinite Dimensional Systems
Computer-Aided Analysis of Difference Schemes for Partial Differential Equations
Computer-Aided Analysis of Difference Schemes for Partial Differential Equations
Central Differencing Based Numerical Schemes for Hyperbolic Conservation Laws with Relaxation Terms
SIAM Journal on Numerical Analysis
Discretization of Unsteady Hyperbolic Conservation Laws
SIAM Journal on Numerical Analysis
On the monotonicity conservation in numerical solutions of the heat equation
Applied Numerical Mathematics
On Discrete Maximum Principles for Linear Equation Systems and Monotonicity of Difference Schemes
SIAM Journal on Matrix Analysis and Applications
High Order Fluctuation Schemes on Triangular Meshes
Journal of Scientific Computing
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
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 II: Applications
SIAM Journal on Scientific Computing
Applied Numerical Mathematics
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The stability and monotonicity of nonlinear difference schemes are studied. The basic approach is to investigate a nonlinear scheme in terms of its corresponding scheme in variations. The advantage of such an approach is that the scheme in variations will always be linear and, hence, enables the investigation of the stability and monotonicity for nonlinear operators using linear patterns. In part I of our two-part paper, we focus on the theoretical background. We establish the notion that the stability (and monotonicity) of a scheme in variations implies the stability (and, respectively, monotonicity) of its original scheme, and that a nonlinear explicit scheme is stable iff (if and only if) the corresponding scheme in variations is stable. Criteria are developed for monotonicity and stability of difference schemes associated with the numerical analysis of systems of partial differential equations (PDEs). The theorem of Friedrichs (1954) is generalized to be applicable to variational schemes with nonsymmetric matrices. High-order interpolation and employment of monotone piecewise cubics in construction of monotone central schemes are considered. As applied to hyperbolic conservation laws with, in general, stiff source terms, we construct a second-order staggered central scheme based on operator-splitting techniques.