Solution and sensitivity analysis of differential-algebraic-Volterra equation systems

• Published in: Computers & chemical engineering Vol. 23; no. 1; pp. 137 - 158
• Main Authors: Mehta, Sanjay, Stewart, Warren E.
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01-01-1998; Elsevier
• Subjects: Applications of mathematics to chemical engineering. Modeling. Simulation. Optimization; Applied sciences; Chemical engineering; Exact sciences and technology; Crystal growth; Sensitivity analysis; Tubular reactor; Differential equation; Fixed bed reactor; Numerical method; Modeling; Equation system; Equation system solving; Adsorption; Algebraic equation; Numerical simulation; Mathematical model; Volterra equation
• ISSN: 0098-1354; 1873-4375
• DOI: 10.1016/S0098-1354(98)00253-1

Step-response modeling of time-dependent systems leads to
weakly singular Volterra equations for the interfacial states, which may be coupled to differential and algebraic equations for the states in an adjoining region. The numerical solution and parametric sensitivity analysis of the resulting system is a challenging problem because of the history-dependent nature of the Volterra states. This paper presents discretization strategies and a solver DAVES (Differential-Algebraic-Volterra Equation Solver) for doing these calculations for systems with regular and weakly singular Volterra kernels. Backward Difference Formulas (BDFs) are used for local discretization of the differential and Volterra operators, while piecewise Gaussian quadrature is employed for the past history terms of the Volterra equations. The solution strategies extend those used in the differential-algebraic solver DDASAC. The new integrator is demonstrated on various chemical engineering problems, including a differential-algebraic-Volterra system encountered in our data-based modeling of packed-tube reactors.