On an algorithm for solving parabolic and elliptic equations

DOI10.1134/S0965542515080035zbMath1327.65159OpenAlexW1609489680MaRDI QIDQ889228

Nicola D'Ascenzo, Valeri Saveliev, Boris N. Chetverushkin

Publication date: 6 November 2015

Published in: Computational Mathematics and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0965542515080035

zbMATH Keywords

stabilityfinite difference methodnumerical examplesparallel computationparabolic equationPoisson equationelliptic equationnumerical algorithmshigh-performance computations

Mathematics Subject Classification ID

Initial-boundary value problems for second-order parabolic equations (35K20) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) 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) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Parallel numerical computation (65Y05) Finite difference methods for boundary value problems involving PDEs (65N06) Computational methods for problems pertaining to astronomy and astrophysics (85-08) PDEs in connection with astronomy and astrophysics (35Q85)

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Cites Work

• Estimates of the difference between approximate solutions of the Cauchy problems for the parabolic diffusion equation and a hyperbolic equation with a small parameter
• Kinetically consistent magnetogasdynamics equations and their use in supercomputer computations
• Explicit schemes and numerical simulation using ultrahigh-performance computer systems
• Hyperbolic type explicit kinetic scheme of magneto gas dynamics for high performance computing systems
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