Abstract and Applied Analysis · 2001 · 56 citations · 0 references
Natural SciencesMathematicsPhysicsComputational MechanicsDifferential EquationsDynamical SystemsDifference EquationsFinite Difference MethodsHyperbolic DynamicsNumerical AnalysisNumerical Methods For Differential EquationsNumerical StabilityFinite Difference SchemesHyperbolic Equation SchemesHyperbolic Partial Differential EquationsInitial Value FormulationInitial Value Problem FormulationInitial Value Problem SolversStability Of Finite Difference Schemes
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.