Numerical Scheme Based on the Implicit Runge-Kutta Method and Spectral Method for Calculating Nonlinear Hyperbolic Evolution Equations
A numerical scheme for nonlinear hyperbolic evolution equations is made based on the implicit Runge-Kutta method and the Fourier spectral method. The detailed discretization processes are discussed in the case of one-dimensional Klein-Gordon equations. In conclusion, a numerical scheme with third-or...
| Published in: | Axioms |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2022-01-01
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| Subjects: | |
| Online Access: | https://www.mdpi.com/2075-1680/11/1/28 |
| Summary: | A numerical scheme for nonlinear hyperbolic evolution equations is made based on the implicit Runge-Kutta method and the Fourier spectral method. The detailed discretization processes are discussed in the case of one-dimensional Klein-Gordon equations. In conclusion, a numerical scheme with third-order accuracy is presented. The order of total calculation cost is <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>O</mi><mo stretchy="false">(</mo><mi>N</mi><msub><mo form="prefix">log</mo><mn>2</mn></msub><mi>N</mi><mo stretchy="false">)</mo></mrow></semantics></math></inline-formula>. As a benchmark, the relations between numerical accuracy and discretization unit size and that between the stability of calculation and discretization unit size are demonstrated for both linear and nonlinear cases. |
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| ISSN: | 2075-1680 |