Search Results - "Runge-Kutta"

The numerical analysis of ordinary differential equations Runge-Kutta and general linear methods by Butcher, John Charles 1933-

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Strong stability preserving Runge-Kutta and multistep time discretizations by Gottlieb, Sigal

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DIFFERENTIAL EQUATIONS An Introduction to Modern Methods and Applications by Brannan, James R., Boyce, William E.

Table of Contents: “…CHAPTER 5 The Laplace Transform -- 5.1 Definition of the Laplace Transform -- 5.2 Properties of the Laplace Transform -- 5.3 The Inverse Laplace Transform -- 5.4 Solving Differential Equations with Laplace Transforms -- 5.5 Discontinuous Functions and Periodic Functions -- 5.6 Differential Equations with Discontinuous Forcing Functions -- 5.7 Impulse Functions -- 5.8 Convolution Integrals and Their Applications -- 5.9 Linear Systems and Feedback Control -- Projects -- 5.P.1 An Electric Circuit Problem -- 5.P.2 The Watt Governor, Feedback Control, and Stability -- CHAPTER 6 Systems of First Order Linear Equations -- 6.1 Definitions and Examples -- 6.2 Basic Theory of First Order Linear Systems -- 6.3 Homogeneous Linear Systems with Constant Coefficients -- 6.4 Nondefective Matrices with Complex Eigenvalues -- 6.5 Fundamental Matrices and the Exponential of a Matrix -- 6.6 Nonhomogeneous Linear Systems -- 6.7 Defective Matrices -- Projects -- 6.P.1 Earthquakes and Tall Buildings -- 6.P.2 Controlling a Spring-Mass System to Equilibrium -- CHAPTER 7 Nonlinear Differential Equations and Stability -- 7.1 Autonomous Systems and Stability -- 7.2 Almost Linear Systems -- 7.3 Competing Species -- 7.4 Predator-Prey Equations -- 7.5 Periodic Solutions and Limit Cycles -- 7.6 Chaos and Strange Attractors: The Lorenz Equations -- Projects -- 7.P.1 Modeling of Epidemics -- 7.P.2 Harvesting in a Competitive Environment -- 7.P.3 The Rossler System -- CHAPTER 8 Numerical Methods -- 8.1 Numerical Approximations: Euler's Method -- 8.2 Accuracy of Numerical Methods -- 8.3 Improved Euler and Runge-Kutta Methods -- 8.4 Numerical Methods for Systems of First Order Equations -- Projects -- 8.P.1 Designing a Drip Dispenser for a Hydrology Experiment -- 8.P.2 Monte Carlo Option Pricing: Pricing Financial Options by Flipping a Coin -- APPENDIX A Matrices and Linear Algebra. …”
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