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Numerical initial value problems in ordinary differential equations by C. William Gear

Numerical initial value problems in ordinary differential equations C. William Gear ebook
ISBN: 0136266061, 9780136266068
Page: 271
Publisher: PH
Format: djvu

Differential equations: First order equations (linear and nonlinear), Higher order linear differential equations with constant coefficients, Cauchy's and Euler's equations, Initial and boundary value problems, Laplace transforms, Solutions of one dimensional heat and wave equations and Laplace Numerical Methods: Numerical solutions of linear and non-linear algebraic equations Integration by trapezoidal and Simpson's rule, single and multi-step methods for differential equations. A numerical method for solving the inverse heat conduction problem without initial value. For the concept of fractional derivative, we will adopt Caputo's definition, which is a modification of the Riemann-Liouville definition and has the advantage of dealing properly with initial value problems. We develop symbolic methods of asymptotic approximations for solutions of linear ordinary differential equations and use them to stabilize numerical calculations. B.; Cheng, J.; Nakagawa, J.; Yamamoto, M. Solve initial value problems for ordinary differential equations Matlab 微分方程的求解_热风暖心_新浪博客,热风暖心, For moderately stiff problems if you need a solution without numerical damping. Goal: To be familiar with the theory of numerical analysis for solving algebraic equations, solution of ordinary and partial differential equations related to engineering problems. Abstract: Scientific computing: Fast Fourier Transform, finite differences, finite elements, spectral method, numerical linear algebra. Solving Systems of Linear Equations; Solving Non-Linear Equations Iteratively; Interpolation; Curve Fitting; Optimization; Numerical Differentiation & Integration; Solving ODEs; Boundary Problems; Solving EigenValue problems. 5, 655–671, 65M32 PDF Clipboard Journal Article . MR2545997 (2010j:35596) Cheng, Jin; Nakagawa, Junichi; Yamamoto, Masahiro; Yamazaki, Tomohiro Uniqueness in an inverse problem for a one-dimensional fractional diffusion equation. Petzold , "Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations" Society for Industrial Mathematics | ISBN: 1999933636 | 3999 | Djvu| 366 pages | 3 MB From the Preface:Differential- algebraic equations (DAE's) arise naturally in many applications, but present numerical and analytical difficulties which do not occur with ordinary differential equations. How solve a system of ordinary differential equation ..an initial value problem .with parameters dependent on time or independent variable? This Demonstration is based on a finite-difference approximation of the Schrödinger equation. Course Contents Review of differential equations, Initial value problem, Taylor series method, Picard's method, Euler's method and its accuracy, Heun's method, Runge-Kutta methods, Solution of the higher order equations, Boundary value problems: Shooting method and its algorithm. Complex variables and applications.