Numerical Analysis on Time Scales / / Svetlin G. Georgiev, Inci M. Erhan.

• Superior document: Title is part of eBook package: De Gruyter DG Plus DeG Package 2022 Part 1
• VerfasserIn: Georgiev, Svetlin G.,; Erhan, Inci M.,
• Place / Publishing House: Berlin ;, Boston : : De Gruyter, , [2022]; ©2022
• Year of Publication: 2022
• Language: English
• Series: De Gruyter Textbook
• Physical Description: 1 online resource (X, 382 p.)

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.

Table of Contents

Frontmatter -- 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