High-performance implementation of a Runge-Kutta finite-difference scheme for the Higgs boson equation in the de Sitter spacetime

DOI10.1016/j.cnsns.2018.07.011OpenAlexW2889275065MaRDI QIDQ2206141

Jacob Banda, Andras Balogh, Karen Yagdjian

Publication date: 21 October 2020

Published in: Communications in Nonlinear Science and Numerical Simulation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1803.01291

zbMATH Keywords

high-performance computationsHiggs boson equation in de Sitter spacetimeunforced damped Duffing equations

Mathematics Subject Classification ID

Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Lattice gravity, Regge calculus and other discrete methods in general relativity and gravitational theory (83C27)

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Cites Work

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• Global existence of the scalar field in de Sitter spacetime
• Solution of non-linear Klein-Gordon equation with a quadratic non-linear term by Adomian decomposition method
• Two finite-difference schemes that preserve the dissipation of energy in a system of modified wave equations
• The semilinear Klein-Gordon equation in de Sitter spacetime
• Analysis of four numerical schemes for a nonlinear Klein-Gordon equation
• Fourth-order compact solution of the nonlinear Klein-Gordon equation
• Lectures on nonlinear hyperbolic differential equations
• A family of low dispersive and low dissipative explicit schemes for flow and noise computations.
• Smooth bump functions and the geometry of Banach spaces. A brief survey
• A numerical solution of the Klein-Gordon equation and convergence of the decomposition method
• The development of Runge-Kutta methods for partial differential equations
• de Sitter tachyons and related topics
• Numerical solution of the nonlinear Klein-Gordon equation using radial basis functions
• Numerical stability of explicit Runge-Kutta finite-difference schemes for the nonlinear Schrödinger equation
• Numerical solution of the nonlinear Klein-Gordon equation
• Numerical study of the blowup/global existence dichotomy for the focusing cubic nonlinear Klein–Gordon equation
• Symbolic Generation of Finite Difference Formulas
• Construction Analysis of Fourth-Order Finite Difference Schemes for the Acoustic Wave Equation in Nonhomogeneous Media
• On the Global Solutions of the Higgs Boson Equation