Abstract and Applied Analysis · 2012 · 16 citations · 16 references
Natural SciencesMathematicsComputational MechanicsDifferential EquationsDynamical SystemsBoundary ConditionsBoundary-value ProblemsDifference EquationsFinite Difference MethodsNumerical StabilityStability TheoryBoundary ProblemBoundary Value Problem SolversFinite Difference SchemesOperator InequalitiesParabolic Boundary-value ProblemsParabolic Equation SchemesParabolic Partial Differential EquationsStability Of Finite Difference Schemes
The boundary value problem of determining the parameter p of a parabolic equation υ ′ ( t ) + A υ ( t ) = f ( t ) + p (0 ≤ t ≤ 1), υ (0) = φ , υ (1) = ψ in an arbitrary Banach space E with the strongly positive operator A is considered. The first order of accuracy stable difference scheme for the approximate solution of this problem is investigated. The well‐posedness of this difference scheme is established. Applying the abstract result, the stability and almost coercive stability estimates for the solution of difference schemes for the approximate solution of differential equations with parameter are obtained.
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