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Numerical Analysis on Time Scales

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Mathematical models cannot be solved using the traditional analytical methods for dynamic equations on time scales. These models must be dealt with using computational methods. This textbook introduces numerical methods for initial value problems for dynamic equations on time scales. Hands-on examples utilizing MATLAB and practical problems illustrate a wide variety of solution techniques.

Author(s): Svetlin G. Georgiev, İnci M. Erhan
Series: De Gruyter Textbook
Publisher: De Gruyter
Year: 2022

Language: English
Pages: 392
City: Berlin

Preface
Contents
1 Polynomial interpolation
2 Numerical integration
3 Piecewise polynomial approximation
4 The Euler method
5 The order 2 Taylor series method – TS(2)
6 The order p Taylor series method – TS (p)
7 Linear multistep methods – LMMs
8 Runge–Kutta methods – RKMs
9 The series solution method – SSM
10 The Adomian polynomials method
11 Weak solutions and variational methods for some classes of linear first-order dynamic systems
12 Variational methods for nonlinear dynamic equations
A Rolle’s theorem
B Fréchet and Gâteaux derivatives
C Pötzsche’s chain rules
D Lebesgue integration. Lp-spaces. Sobolev spaces
E Mazur’s theorem
Bibliography
Index