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Identification of parameters in initial value problems for ordinary differential equations

Chleboun, Jan, Mikeš, Karel (2015)

Programs and Algorithms of Numerical Mathematics

Scalar parameter values as well as initial condition values are to be identified in initial value problems for ordinary differential equations (ODE). To achieve this goal, computer algebra tools are combined with numerical tools in the MATLAB environment. The best fit is obtained through the minimization of the summed squares of the difference between measured data and ODE solution. The minimization is based on a gradient algorithm where the gradient of the summed squares is calculated either numerically...

Implicit Runge-Kutta methods for transferable differential-algebraic equations

M. Arnold (1994)

Banach Center Publications

The numerical solution of transferable differential-algebraic equations (DAE’s) by implicit Runge-Kutta methods (IRK) is studied. If the matrix of coefficients of an IRK is non-singular then the arising systems of nonlinear equations are uniquely solvable. These methods are proved to be stable if an additional contractivity condition is satisfied. For transferable DAE’s with smooth solution we get convergence of order m i n ( k E , k I + 1 ) , where k E is the classical order of the IRK and k I is the stage order. For transferable...

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