A note on the difference schemes for hyperbolic equations

By Allaberen Ashyralyev, P. Sobolevskiĭ. 2001

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The initial value problem for hyperbolic equations d 2 u ( t ) / d t 2 + A u ( t ) = f ( t ) ( 0 ≤ t ≤ 1 ) , u ( 0 ) = φ , u ′ ( 0 ) = ψ , in a Hilbert space H is considered. The first and second order accuracy difference schemes generated by the integer power of A approximately solving this initial value problem are presented. The stability estimates for the solution of these difference schemes are obtained.

Subfields: Applied Mathematics, Numerical Analysis

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