Modified iterated Crank-Nicolson method with improved accuracy for advection equations

DOI10.1007/s11075-023-01619-5OpenAlexW4385331976MaRDI QIDQ6202784

Jinjie Liu, Qiqi Tran

Publication date: 26 March 2024

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11075-023-01619-5

zbMATH Keywords

Burgers' equationGross-Pitaevskii equationiterated Crank-Nicolson method

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) 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) NLS equations (nonlinear Schrödinger equations) (35Q55) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Finite difference methods for boundary value problems involving PDEs (65N06) Second-order semilinear hyperbolic equations (35L71) First-order hyperbolic equations (35L02)

Cites Work

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• Computational methods for the dynamics of the nonlinear Schrödinger/Gross-Pitaevskii equations
• Fortran programs for the time-dependent Gross-Pitaevskii equation in a fully anisotropic trap
• On iterated Crank-Nicolson methods for hyperbolic and parabolic equations
• Mathematical theory and numerical methods for Bose-Einstein condensation
• Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov's method
• Total variation diminishing Runge-Kutta schemes

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