Convergent Numerical Schemes for the Compressible Hyperelastic Rod Wave Equation

Details Convergent Numerical Schemes for the Compressible Hyperelastic Rod Wave Equation Convergent Numerical Schemes for the Compressible Hyperelastic Rod Wave Equation

2011-09-09

arxiv.org/abs/1109.2005v1

Mathematics

Numerical Analysis

Scientific paper

We propose a fully discretised numerical scheme for the hyperelastic rod wave equation on the line. The convergence of the method is established. Moreover, the scheme can handle the blow-up of the derivative which naturally occurs for this equation. By using a time splitting integrator which preserves the invariants of the problem, we can also show that the scheme preserves the positivity of the energy density.

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