Read online book Introduction to Numerical Methods for Time Dependent Differential Equations by Heinz-Otto Kreiss in EPUB, DOC, FB2
9781118838952 English 1118838955 Introduces both the fundamentals of time dependent differential equations and their numerical solutions"Introduction to Numerical Methods for Time Dependent Differential Equations "delves into the underlying mathematical theory needed to solve time dependent differential equations numerically. Written as a self-contained introduction, the book is divided into two parts to emphasize both ordinary differential equations (ODEs) and partial differential equations (PDEs).Beginning with ODEs and their approximations, the authors provide a crucial presentation of fundamental notions, such as the theory of scalar equations, finite difference approximations, and the Explicit Euler method. Next, a discussion on higher order approximations, implicit methods, multistep methods, Fourier interpolation, PDEs in one space dimension as well as their related systems is provided."Introduction to Numerical Methods for Time Dependent Differential Equations "features: A step-by-step discussion of the procedures needed to prove the stability of difference approximationsMultiple exercises throughout with select answers, providing readers with a practical guide to understanding the approximations of differential equationsA simplified approach in a one space dimensionAnalytical theory for difference approximations that is particularly useful to clarify procedures"Introduction to Numerical Methods for Time Dependent Differential Equations "is an excellent textbook for upper-undergraduate courses in applied mathematics, engineering, and physics as well as a useful reference for physical scientists, engineers, numerical analysts, and mathematical modelers who use numerical experiments to test designs or predict and investigate phenomena from many disciplines., This book is divided into two parts: Part One, Ordinary Differential Equations and their Approximations and Part Two, Partial Differential Equations and their Approximations .Part One consists ofChapters 1 to6 anddeals with ordinary differential equations (ODE) and their approximations. Chapter 1 containsa simple presentation of the fundamental ideas in the theory of scalar equations. Chapter2 presentsthe core of the first part of the book and iswhere most of the important concepts on finite difference approximations are introduced and explained for the most basic method of all, the Explicit Euler method. The remainingchapters in Part One deal with higher order approximations, implicit methods, multistep methods, and systems of ODE.Part Twoconsists of Chapters 7-11 and addresses partial differential equations in one space dimension and their approximations. The basics of Fourier series and interpolation are presented in Chapter 7.Chapters 8, 9, and 10 are devoted to the concepts of well posedness and numerical approximations for both Cauchy problems and initial-boundary value problems. The authorsdiscuss the three basic equations: the one-way wave equation (or advection equation); the heat equation; and the wave equation. Chapter11develops the idea of "when"and "why" nonlinear differential problems can be thought as perturbations of numerically computed solutions, thus making the approximations meaningful. Topical coverages includes: first order scalar equations; the method of Euler; higher order methods; the implicit Euler methods, two step and multistep methods; systems of differential equations; Fourier series and interpolation; 1-periodic solutions; approximations of 1-periodic solutions; linear initial-boundary value problems; and nonlinear problems., This introductory, self-contained book emphasizes both the fundamentals of time-dependent differential equations and the numerical solutions of these equations.The book is divided into two parts: Part One deals with ordinary differential equations (ODE) and their approximations. Part Two addresses partial differential equations in one space dimension and their approximations. Topical coverages includes: first order scalar equations; the method of Euler; higher order methods; the implicit Euler methods, two step and multistep methods; systems of differential equations; Fourier series and interpolation; 1-periodic solutions; approximations of 1-periodic solutions; linear initial-boundary value problems; and nonlinear problems."Introduction to Numerical Methods for Time Dependent Differential Equations" Provides topical coverage in a very simplified manner and only in a one space dimensionPresents the analytic theory and translates it into a theory for difference approximationsContains worked out solutions to select answers at the end of the bookOffers an Instructor's Solution Manual containing the complete solutions (available via written request to the Publisher)Classroom-tested and based on course notes used at both UCLA and the National University of Cordoba
9781118838952 English 1118838955 Introduces both the fundamentals of time dependent differential equations and their numerical solutions"Introduction to Numerical Methods for Time Dependent Differential Equations "delves into the underlying mathematical theory needed to solve time dependent differential equations numerically. Written as a self-contained introduction, the book is divided into two parts to emphasize both ordinary differential equations (ODEs) and partial differential equations (PDEs).Beginning with ODEs and their approximations, the authors provide a crucial presentation of fundamental notions, such as the theory of scalar equations, finite difference approximations, and the Explicit Euler method. Next, a discussion on higher order approximations, implicit methods, multistep methods, Fourier interpolation, PDEs in one space dimension as well as their related systems is provided."Introduction to Numerical Methods for Time Dependent Differential Equations "features: A step-by-step discussion of the procedures needed to prove the stability of difference approximationsMultiple exercises throughout with select answers, providing readers with a practical guide to understanding the approximations of differential equationsA simplified approach in a one space dimensionAnalytical theory for difference approximations that is particularly useful to clarify procedures"Introduction to Numerical Methods for Time Dependent Differential Equations "is an excellent textbook for upper-undergraduate courses in applied mathematics, engineering, and physics as well as a useful reference for physical scientists, engineers, numerical analysts, and mathematical modelers who use numerical experiments to test designs or predict and investigate phenomena from many disciplines., This book is divided into two parts: Part One, Ordinary Differential Equations and their Approximations and Part Two, Partial Differential Equations and their Approximations .Part One consists ofChapters 1 to6 anddeals with ordinary differential equations (ODE) and their approximations. Chapter 1 containsa simple presentation of the fundamental ideas in the theory of scalar equations. Chapter2 presentsthe core of the first part of the book and iswhere most of the important concepts on finite difference approximations are introduced and explained for the most basic method of all, the Explicit Euler method. The remainingchapters in Part One deal with higher order approximations, implicit methods, multistep methods, and systems of ODE.Part Twoconsists of Chapters 7-11 and addresses partial differential equations in one space dimension and their approximations. The basics of Fourier series and interpolation are presented in Chapter 7.Chapters 8, 9, and 10 are devoted to the concepts of well posedness and numerical approximations for both Cauchy problems and initial-boundary value problems. The authorsdiscuss the three basic equations: the one-way wave equation (or advection equation); the heat equation; and the wave equation. Chapter11develops the idea of "when"and "why" nonlinear differential problems can be thought as perturbations of numerically computed solutions, thus making the approximations meaningful. Topical coverages includes: first order scalar equations; the method of Euler; higher order methods; the implicit Euler methods, two step and multistep methods; systems of differential equations; Fourier series and interpolation; 1-periodic solutions; approximations of 1-periodic solutions; linear initial-boundary value problems; and nonlinear problems., This introductory, self-contained book emphasizes both the fundamentals of time-dependent differential equations and the numerical solutions of these equations.The book is divided into two parts: Part One deals with ordinary differential equations (ODE) and their approximations. Part Two addresses partial differential equations in one space dimension and their approximations. Topical coverages includes: first order scalar equations; the method of Euler; higher order methods; the implicit Euler methods, two step and multistep methods; systems of differential equations; Fourier series and interpolation; 1-periodic solutions; approximations of 1-periodic solutions; linear initial-boundary value problems; and nonlinear problems."Introduction to Numerical Methods for Time Dependent Differential Equations" Provides topical coverage in a very simplified manner and only in a one space dimensionPresents the analytic theory and translates it into a theory for difference approximationsContains worked out solutions to select answers at the end of the bookOffers an Instructor's Solution Manual containing the complete solutions (available via written request to the Publisher)Classroom-tested and based on course notes used at both UCLA and the National University of Cordoba