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Billingham , S. Finding and interpreting the solutions of differential equations is a central and essential part of applied mathematics. This book aims to enable the reader to develop the required skills needed for a thorough understanding of the subject.

Application of one‐step method to parameter estimation in ODE models

The authors focus on the business of constructing solutions analytically, and interpreting their meaning, using rigorous analysis where needed. There are many worked examples based on interesting and unusual real world problems. A large selection of exercises is provided, including several lengthier projects, some of which involve the use of MATLAB. The coverage is broad, ranging from basic second-order ODEs and PDEs, through to techniques for nonlinear differential equations, chaos, asymptotics and control theory.

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This broad coverage, the authors' clear presentation and the fact that the book has been thoroughly class-tested will increase its attraction to undergraduates at each stage of their studies. Legendre Functions. The target audience primarily comprises applied researchers and practitioners in engineering, but the book may also be beneficial for graduate students.

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Real data examples In this section, we study several real data examples. Table 5 Parameter estimates for model Equation 20 obtained in the literature. Table 7 Point estimates for the parameters of model Equation 20 based on the real data of table 39 in Bodenstein Figure 6. Figure 7. Table 8 Point estimates for the parameters of model Equation 21 based on the real data from Box et al. Conclusions Parameter estimation for ODEs is a challenging problem. Appendix A. Proof of Theorem 1 A.

Appendix B. Integral estimator B. Appendix C. Goodwin's oscillator C. Notes Dattner I. Footnotes 1 Note that Varah gives five different parameter estimates corresponding to different values of the smoothing parameter used in his method.


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Of these estimates, we report only the first pair and refer to Table 4 in Varah for the remaining ones. References Bellman R. Quasilinearization and the estimation of chemical rate constants from raw kinetic data.

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Differential equation introduction - First order differential equations - Khan Academy

Parameter estimation for differential equations: a generalized smoothing approach. Robust parameter estimation for the Ornstein—Uhlenbeck process. The solution of a set of reaction rate equations In Walsh J. London, New York: Academic Press, pp.

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Novel metaheuristic for parameter estimation in nonlinear dynamic biological systems. BMC Bioinformatics , 7 , Numerical data fitting in dynamical systems , Applied Optimization, Vol. Journal of the American Statistical Association , 87 , — PLoS Computational Biology , 9 , e Discussion of parameter estimation in biological modelling: algorithms for estimation and evaluation of the estimates.

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