Trapezoidal and midpoint splittings for initial-boundary value problems

DOI10.1090/S0025-5718-98-00984-3zbMath0896.65060MaRDI QIDQ4396449

Willem H. Hundsdorfer

Publication date: 14 June 1998

Published in: Mathematics of Computation (Search for Journal in Brave)

zbMATH Keywords

stabilityinitial-boundary value problemssplitting methods

Mathematics Subject Classification ID

Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Initial value problems for second-order parabolic equations (35K15) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20)

Related Items (17)

Fractional step Runge-Kutta methods for time dependent coefficient parabolic problems ⋮ Implicit-explicit multistep formulations for finite element discretisations using continuous interior penalty ⋮ A positive splitting method for mixed hyperbolic-parabolic systems ⋮ Application of discontinuous Galerkin methods for reaction-diffusion systems in developmental biology ⋮ The positivity of low-order explicit Runge-Kutta schemes applied in splitting methods. ⋮ A note on stability of the Douglas splitting method ⋮ Using splitting methods in continuous digester modeling ⋮ Approximate analytical solutions of Schnakenberg systems by homotopy analysis method ⋮ Approximate factorization for time-dependent partial differential equations ⋮ Stability results for fractional step discretizations of time dependent coefficient evolutionary problems ⋮ The use of splitting methods in the numerical simulation of reacting flows ⋮ The modeling of realistic chemical vapor infiltration/deposition reactors ⋮ Stability results for linearly implicit fractional step discretizations of nonlinear time dependent parabolic problems ⋮ Linearly implicit splitting methods for higher space-dimensional parabolic differential equations ⋮ Additive Runge-Kutta methods for the resolution of linear parabolic problems ⋮ Accuracy and stability of splitting with stabilizing corrections ⋮ Stability of W-methods with applications to operator splitting and to geometric theory

Cites Work

• Convergence of method of lines approximations to partial differential equations
• B-convergence of the implicit midpoint rule and the trapezoidal rule
• An implicit finite-difference algorithm for hyperbolic systems in conservation-law form
• One-step splitting methods for semi-discrete parabolic equations
• Interior estimates for time discretizations of parabolic equations
• Stability and Convergence of the Peaceman-Rachford ADI Method for Initial-Boundary Value Problems
• Single step methods for inhomogeneous linear differential equations in Banach space
• Unconditional Convergence of Some Crank-Nicolson Lod Methods for Initial- Boundary Value Problems
• A note on stability of the Douglas splitting method
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