Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Discretization based indices for semilinear partial differential algebraic equations
Applied Numerical Mathematics - Selected papers on eighth conference on the numerical treatment of differential equations 1-5 September 1997, Alexisbad, Germany
A Differentiation Index for Partial Differential-Algebraic Equations
SIAM Journal on Scientific Computing
Index Concepts for Linear Mixed Systems of Differential-Algebraic and Hyperbolic-Type Equations
SIAM Journal on Scientific Computing
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For numerous problems in science and engineering a refined modeling approach leads to initial-boundary value problems for partial differential-algebraic equations (PDAEs). The paper investigates linear PDAEs from the point of view of weakly differentiable in space solutions. The appropriate treatment of boundary conditions is obtained by the requirement that the spatial differential operator has to satisfy a Gårding-type inequality in suitable function spaces. Based on this, an index concept extending the classical perturbation index is introduced.