Uniformly high order accurate essentially non-oscillatory schemes, 111
Journal of Computational Physics
Numerical experiments on the accuracy of ENO and modified ENO schemes
Journal of Scientific Computing
Weighted essentially non-oscillatory schemes
Journal of Computational Physics
A Mixed Finite Element--Finite Volume Formulation of the Black-Oil Model
SIAM Journal on Scientific Computing
The random projection method for hyperbolic conservation laws with stiff reaction terms
Journal of Computational Physics
A triangle-based unstructured finite-volume method for chemically reactive hypersonic flows
Journal of Computational Physics
Partially Implicit BDF2 Blends for Convection Dominated Flows
SIAM Journal on Numerical Analysis
Implicit-explicit time stepping with spatial discontinuous finite elements
Applied Numerical Mathematics
Applied Numerical Mathematics - Special issue: Applied scientific computing - Grid generation, approximated solutions and visualization
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
SIAM Journal on Numerical Analysis
Mesh locking effects in the finite volume solution of 2-D anisotropic diffusion equations
Journal of Computational Physics
DIMEX Runge-Kutta finite volume methods for multidimensional hyperbolic systems
Mathematics and Computers in Simulation
A unified treatment of boundary conditions in least-square based finite-volume methods
Computers & Mathematics with Applications
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A class of conservative methods is developed in the more general framework of cell-centered upwind differences to approximate numerically the solution of one-dimensional non-linear conservation laws with (possibly) stiff reaction source terms. These methods are based on a non-oscillatory piecewise linear polynomial representation of the discrete solution within any mesh interval to compute pointwise solution values. The piecewise linear approximate solution is obtained by approximating the cell average of the analytical solution and the solution slope in every mesh cell. These two quantities are evolved in time by solving a set of discrete equations that are suitably designed to ensure formal second-order consistency. Several numerical tests which are taken from literature illustrate the performance of the method in solving non-stiff and stiff convection-reaction equations in conservative form.