Abstract
The abstract Cauchy problem for the hyperbolic equation in a Hilbert space H with self-adjoint positive definite operator A is considered. The third and fourth orders of accuracy difference schemes for the approximate solution of this problem are presented. The stability estimates for the solutions of these difference schemes are established. A finite difference method and some results of numerical experiments are presented in order to support theoretical statements.
Keywords
Mathematics
Hyperbolic partial differential equation
Partial differential equation
Hilbert space
Cauchy problem
Finite difference
Mathematical analysis
Ordinary differential equation
Stability (learning theory)
Finite difference method
Finite difference coefficient
Operator (biology)
FTCS scheme
Applied mathematics
Initial value problem
Differential equation
Finite element method
Mixed finite element method
Subject Areas
Differential Equations and Numerical Methods
·Numerical Analysis ·Physical Sciences
Advanced Mathematical Physics Problems
·Mathematical Physics ·Physical Sciences
Differential Equations and Boundary Problems
·Applied Mathematics ·Physical Sciences
Citations by Year
2012: 1
2014: 1
2015: 3
2017: 1
2018: 2
2021: 1
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