{"product_id":"numerical-solution-of-odes-9780470042946","title":"Numerical Solution of ODEs","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis precise and highly readable book provides a complete and concise introduction to classical topics in the numerical solution of ordinary differential equations (ODEs). It contains many up-to-date references to both analytical and numerical ODE literature while offering new unifying views on different problem classes.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"An accompanying Web site offers access to more than ten MATLAB programs.\" \u003ci\u003e(CHOICE,\u003c\/i\u003e December 2009)\u003cbr\u003e \u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface.  \u003cp\u003eIntroduction.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1. Theory of differential equations: an introduction.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 General solvability theory.\u003c\/p\u003e \u003cp\u003e1.2 Stability of the initial value problem.\u003c\/p\u003e \u003cp\u003e1.3 Direction fields.\u003c\/p\u003e \u003cp\u003eProblems.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2. Euler’s method.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Euler’s method.\u003c\/p\u003e \u003cp\u003e2.2 Error analysis of Euler’s method.\u003c\/p\u003e \u003cp\u003e2.3 Asymptotic error analysis.\u003c\/p\u003e \u003cp\u003e2.3.1 Richardson extrapolation.\u003c\/p\u003e \u003cp\u003e2.4 Numerical stability.\u003c\/p\u003e \u003cp\u003e2.4.1 Rounding error accumulation.\u003c\/p\u003e \u003cp\u003eProblems.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3. Systems of differential equations.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Higher order differential equations.\u003c\/p\u003e \u003cp\u003e3.2 Numerical methods for systems.\u003c\/p\u003e \u003cp\u003eProblems.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4. The backward Euler method and the trapezoidal method.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 The backward Euler method.\u003c\/p\u003e \u003cp\u003e4.2 The trapezoidal method.\u003c\/p\u003e \u003cp\u003eProblems.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5. Taylor and Runge-Kutta methods.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Taylor methods.\u003c\/p\u003e \u003cp\u003e5.2 Runge-Kutta methods.\u003c\/p\u003e \u003cp\u003e5.3 Convergence, stability, and asymptotic error.\u003c\/p\u003e \u003cp\u003e5.4 Runge-Kutta-Fehlberg methods.\u003c\/p\u003e \u003cp\u003e5.5 Matlab codes.\u003c\/p\u003e \u003cp\u003e5.6 Implicit Runge-Kutta methods.\u003c\/p\u003e \u003cp\u003eProblems.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6. Multistep methods.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Adams-Bashforth methods.\u003c\/p\u003e \u003cp\u003e6.2 Adams-Moulton methods.\u003c\/p\u003e \u003cp\u003e6.3 Computer codes.\u003c\/p\u003e \u003cp\u003eProblems.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7. General error analysis for multistep methods.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Truncation error.\u003c\/p\u003e \u003cp\u003e7.2 Convergence.\u003c\/p\u003e \u003cp\u003e7.3 A general error analysis.\u003c\/p\u003e \u003cp\u003eProblems.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8. Stiff differential equations.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 The method of lines for a parabolic equation.\u003c\/p\u003e \u003cp\u003e8.2 Backward differentiation formulas.\u003c\/p\u003e \u003cp\u003e8.3 Stability regions for multistep methods.\u003c\/p\u003e \u003cp\u003e8.4 Additional sources of difficulty.\u003c\/p\u003e \u003cp\u003e8.5 Solving the finite difference method.\u003c\/p\u003e \u003cp\u003e8.6 Computer codes.\u003c\/p\u003e \u003cp\u003eProblems.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9. Implicit RK methods for stiff differential equations.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Families of implicit Runge-Kutta methods.\u003c\/p\u003e \u003cp\u003e9.2 Stability of Runge-Kutta methods.\u003c\/p\u003e \u003cp\u003e9.3 Order reduction.\u003c\/p\u003e \u003cp\u003e9.4 Runge-Kutta methods for stiff equations in practice.\u003c\/p\u003e \u003cp\u003eProblems.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10. Differential algebraic equations.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Initial conditions and drift.\u003c\/p\u003e \u003cp\u003e10.2 DAEs as stiff differential equations.\u003c\/p\u003e \u003cp\u003e10.3 Numerical issues: higher index problems.\u003c\/p\u003e \u003cp\u003e10.4 Backward differentiation methods for DAEs.\u003c\/p\u003e \u003cp\u003e10.5 Runge-Kutta methods for DAEs.\u003c\/p\u003e \u003cp\u003e10.6 Index three problems from mechanics.\u003c\/p\u003e \u003cp\u003e10.7 Higher index DAEs.\u003c\/p\u003e \u003cp\u003eProblems.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11. Two-point boundary value problems.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 A finite difference method.\u003c\/p\u003e \u003cp\u003e11.2 Nonlinear two-point boundary value problems.\u003c\/p\u003e \u003cp\u003eProblems.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e12. Volterra integral equations.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e12.1 Solvability theory.\u003c\/p\u003e \u003cp\u003e12.2 Numerical methods.\u003c\/p\u003e \u003cp\u003e12.3 Numerical methods - Theory.\u003c\/p\u003e \u003cp\u003eProblems.\u003c\/p\u003e \u003cp\u003eAppendix A. Taylor’s theorem.\u003c\/p\u003e \u003cp\u003eAppendix B. Polynomial interpolation.\u003c\/p\u003e \u003cp\u003eBibliography.\u003c\/p\u003e \u003cp\u003eIndex.\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49402270089559,"sku":"9780470042946","price":91.76,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780470042946.jpg?v=1730479900","url":"https:\/\/bookcurl.com\/products\/numerical-solution-of-odes-9780470042946","provider":"Book Curl","version":"1.0","type":"link"}