Numerical Analysis on Time Scales
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Svetlin G. Georgiev
and Inci M. Erhan
About this book
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.
This textbook discusses the design, analysis and applications of computational techniques for dynamic equations on time scales. Hands-on examples utilizing MATLAB are provided as well as end of chapter problems.
Author / Editor information
Svetlin G. Georgiev
(born 1974, Bulgaria) has worked in various areas of mathematics. His current focus: harmonic analysis, functional analysis, partial differential equations, ordinary differential equations, Clifford and quaternion analysis, integral equations, dynamic calculus on time scales.
Inci M. Erhan
(born 1971, Bulgaria) is a full professor of mathematics at Atilim University, Turkey. Her areas of research include numerical solutions of differential equations and dynamic equations on time scales, fixed point theory and its applications.
Topics
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Frontmatter
I -
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Preface
V -
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Contents
VII -
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1 Polynomial interpolation
1 -
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2 Numerical integration
44 -
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3 Piecewise polynomial approximation
89 -
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4 The Euler method
122 -
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5 The order 2 Taylor series method – TS(2)
149 -
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6 The order p Taylor series method – TS (p)
168 -
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7 Linear multistep methods – LMMs
188 -
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8 Runge–Kutta methods – RKMs
204 -
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9 The series solution method – SSM
227 -
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10 The Adomian polynomials method
249 -
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11 Weak solutions and variational methods for some classes of linear first-order dynamic systems
266 -
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12 Variational methods for nonlinear dynamic equations
281 -
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A Rolle’s theorem
303 -
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B Fréchet and Gâteaux derivatives
309 -
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C Pötzsche’s chain rules
319 -
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D Lebesgue integration. Lp-spaces. Sobolev spaces
329 -
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E Mazur’s theorem
377 -
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Bibliography
379 -
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Index
381
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