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This paper is concerned with solving the problem of identifying the control vector problem for a fractional multi-order system of nonlinear ordinary differential equations (ODEs). We describe a quasilinearization approach, based on minimization of a quadratic functional, to compute the values of the unknown parameter vector. Numerical algorithm combining the method with appropriate fractional derivative approximation on graded mesh is applied to SIS and SEIR problems to illustrate the efficiency and accuracy. Tikhonov regularization is implemented to improve the convergence. Results from computations, both with noisy-free and noisy data, are provided and discussed. Simulations with real data are also performed. [ABSTRACT FROM AUTHOR]

A time stepping quasilinearization approach to the mixed (or coupled) form of one and two dimensional Richards' equations is developed. For numerical solution of the linear ordinary differential equation (ODE) for 1D case and elliptic for 2D case, obtained after this semidiscretization, a finite volume method is used for direct problems arising on each time level. Next, we propose a version of the decomposition method for the numerical solution of the inverse ODE and 2D elliptic boundary problems. Computational results for some soil types and its related parameters reported in the literature are presented. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, on the basis of Newton’s method, we propose a fast quasilinearization numerical scheme, coupled with Rothe’s method, for fully nonlinear parabolic equations. General conditions that provide quadratic, uniform and monotone convergence of the quasilinearization method (QLM) of solving fully nonlinear ordinary differential equations that arise on each time level, are formulated and elaborated. The convergence of QLM and its rate are examined numerically, on a simple test example with an exact solution. The first few iterations already provide extremely accurate and stable numerical results. The second goal is to consider three applications of the proposed schemes in financial mathematics. Namely, numerical results for three nonlinear problems of optimal investment are presented and discussed. The numerical experiments of the last problem are based on the data from statistic information of the Bulgarian National Bank and Bratislava Interbank. [Copyright &y& Elsevier]