Georgiev S. Numerical Analysis on Time Scales 2022

Textbook in PDF format

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.
Preface
Polynomial interpolation
Numerical integration
Piecewise polynomial approximation
The Euler method
The order 2 Taylor series method – TS(2)
The order p Taylor series method – TS (p)
Linear multistep methods – LMMs
Runge–Kutta methods – RKMs
The series solution method – SSM
The Adomian polynomials method
Weak solutions and variational methods for some classes of linear first-order dynamic systems
Variational methods for nonlinear dynamic equations
Rolle’s theorem
Fréchet and Gâteaux derivatives
Pötzsche’s chain rules
Lebesgue integration. Lp-spaces. Sobolev spaces
Mazur’s theorem
Bibliography
Index