Numerical Solution of Ordinary Differential Equations
Added On :
Author :
For :
Numerical Solution of Ordinary Differential Equations By E. Suli.
Contents
1 Picard?s theorem 1
2 One-step methods 4
2.1 Euler?s method and its relatives: the θ-method . . . . . . . . . . . . . . . . . . . . 4
2.2 Error analysis of the θ-method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.3 General explicit one-step method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.4 Runge?Kutta methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.5 Absolute stability of Runge?Kutta methods . . . . . . . . . . . . . . . . . . . . . . 19
3 Linear multi-step methods 21
3.1 Construction of linear multi-step methods . . . . . . . . . . . . . . . . . . . . . . . 22
3.2 Zero-stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.3 Consistency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.4 Convergence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.4.1 Necessary conditions for convergence . . . . . . . . . . . . . . . . . . . . . . 30
3.4.2 Sufficient conditions for convergence . . . . . . . . . . . . . . . . . . . . . . 33
3.5 Maximum order of a zero-stable linear multi-step method . . . . . . . . . . . . . . 37
3.6 Absolute stability of linear multistep methods . . . . . . . . . . . . . . . . . . . . . 43
3.7 General methods for locating the interval of absolute stability . . . . . . . . . . . . 45
3.7.1 The Schur criterion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.7.2 The Routh?Hurwitz criterion . . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.8 Predictor-corrector methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.8.1 Absolute stability of predictor-corrector methods . . . . . . . . . . . . . . . 50
3.8.2 The accuracy of predictor-corrector methods . . . . . . . . . . . . . . . . . 52
4 Stiff problems 53
4.1 Stability of numerical methods for stiff systems . . . . . . . . . . . . . . . . . . . . 54
4.2 Backward differentiation methods for stiff systems . . . . . . . . . . . . . . . . . . 57
4.3 Gear?s method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
5 Nonlinear Stability 59
6 Boundary value problems 62
6.1 Shooting methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
6.1.1 The method of bisection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
6.1.2 The Newton?Raphson method . . . . . . . . . . . . . . . . . . . . . . . . . 63
6.2 Matrix methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
6.2.1 Linear boundary value problem . . . . . . . . . . . . . . . . . . . . . . . . . 66
6.2.2 Nonlinear boundary value problem . . . . . . . . . . . . . . . . . . . . . . . 69
6.3 Collocation method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
Tags : Book Numerical Solution of Ordinary Differential Equations Pdf download Book Numerical Solution of Ordinary Differential Equations by E. Suli. Pdf download Author E. Suli. written the book namely Numerical Solution of Ordinary Differential Equations Author E. Suli. Pdf download Study material of Numerical Solution of Ordinary Differential Equations Pdf download Lacture Notes of Numerical Solution of Ordinary Differential Equations Pdf
Last 30 days 412 reviews
OTHER SUGEST TOPIC
Recent New Topics :
| Schaum's Outline of Theory And Problems of Strength of Materials William A Nash | | Mechanics and Strength of Materials Vitor Dias da Silva | | Solution of All Unsolved problem in Shigley's Mechanical Engineering Design Richard G Budynas, J Keith Nisbett | | Shigley's Mechanical Engineering Design Richard G Budynas, J Keith Nisbett | | Total Quality Management in Education Edward Sallis | | Process Planning and Cost Estimation R. Kesavan, C. Elanchezhian, B. Vijaya Ramnath | | Introduction to Mechatronics | | Introduction to Basic Manufacturing Process and Workshop Technology Rajender Singh | | Principles Of Heat Transfer Frank Kreith,Raj M. Manglik, Mark S. Bohn | | Introduction to Heat Transfer Vedat S Arpaci, Ahmet Selamet, Shu Hsin Kao | | Heat Transfer - Engineering Applications Vyacheslav S. Vikhrenko. | | Heat and Mass Transfer Frank Kreith, Robert F. Boehm | | Fundamentals of Heat and Mass Transfer C P Kothandaraman | | Introduction to Fluid Mechanics Edward J. Shaughnessy, Jr., Ira M. Katz, James P. Schaffer | | Basic Concepts And Definitions - Easy Notes | | Thermodynamics An Engineering Approach Yunus A Cengel, Michael A Boles | | Engineering Thermodynamics R K Rajput | | Basic And Applied Thermodynamics P K Nag | | Vector Mechanics for Engineers Statics Ferdinand P Beer, E Russell Johnston, Elliot R Eisenberg | | Engineering Mechanics - Statics : Lecture Notes R. Ganesh Narayanan | | Engineering Mechanic Statics R C Hibbler | | A TextBook Of Machine Design R S Khurmi, J K Gupta | | Bolted Joint Design FEDS | | Design Of Temporary Connections | | The Quadratic Eigenvalue Francoise, Meerbergen | | Initial Value Problems for Ordinary Differential Equations - Lecture Notes Michael T. Heath | | Partial Differential Equations With Fourier Series And Boundary Value Problems Nakhle H. Asmar | | Partial Differential Equation Toolbox - For Use with MATLAB | | Partial Differential Equations Robert | | Partial Differential Equations Jerry L. Kazdan | | Partial Differential Equations in Action From Modelling to Theory Sandro Salsa | | Partial Differential Equations: Graduate Level Problems and Solutions Igor Yanovsky | | Numerical Solution of Singular Eigenvalue | | Numerical Solution of Ordinary Differential Equations E. Suli. | | Numerical Methods for Differential Equations Ya Yan Lu | | Numerical Methods For Ordinary Differential Equations | | Numerical Methods - Lecture Notes R. Verfurth | | Numerical Differentiation & Integration - Numerical Differentiation I R L Burden & J D Faires | | Numerical Differentiation and Integration - Lecture Notes | | Numerical Differentiation and Integration Tutorial | | Numerical Analysis - Lecture Notes Doron Levy | | Numerical Analysis and Computing - Lecture Notes | | Notes on Differential Equations Robert E. Terrell | | Lectures on Diffusion Problems and Partial Differential Equations S. R. S. Varadhan | | Lectures In Basic Computational Numerical Analysis J. M. McDonough | | Introduction to Variational Methods in Partial Differential Equations and Applications Baisheng Yan | | Introduction to Partial Differential Equations John Douglas Moore | | Introduction to Numerical Analysis Doron Levy | | Introduction To Interpolation - Lecture Notes | | Introduction to Differential Equations Jeffrey R. Chasnov | | Interpolation - Easy Notes | | Interpolation & Polynomial Approximation - Data Approximation & Neville's Method | | Interpolation and Curve Fitting | | Handbook Of Linear Partial Differential Equations For Engineers And Scientists Andrei D. Polyanin | | Fundamental Numerical Methods and Data Analysis George W. Collins, II | | Functional Analysis, Sobolev Spaces and Partial Differential Equations Haim Brezis. | | Differential Equations Amol Sasane | | Differential-Algebraic Equations (DAEs) and numerical methods | | Computational Methods in Astrophysics - Ordinary Differential Equations - Cosmological Models Joachim Puls, Fabian Heitsch | | A Students Guide to Fourier Transforms with Applications in Physics and Engineering J. F. James | | Applications of Wavelets to Partial Differential Equations | | A numerical study of the Schrodinger-Newton equations Richard Harrison | | An Introduction to Fourier Analysis - Fourier Series, Partial Differential Equations and Fourier Transforms | | Z Transforms - Easy Notes | | z-Transform - Lecture Seminar Slide Notes | | Waves in Music: Applications of Partial Differential Equations Ed Cottrell | | Undergraduate Notes in Mathematics Marcel B. Finan | | The Z Transform - Lecture Notes | | The One-Side z Transform - Lecture Notes | | Solution of Partial Differential Equations with Electrical Equivalent Analogy | | Review of z transforms and Difference Equation | | Partial Differential Equations and waves - Lecture Notes Michael Brady | | n Multi dimensional Fourier Transform | | Lectures On Fourier Series | | Introduction to the Fourier Series | | Fourier Transform - Lecture Notes | | Fourier series - tutorial Graham S McDonald | | Fourier Series and Transforms - Lecture Note | | Fourier Series and Transform - Lecture Notes | | Disccrete Time Systems and Z Transforms | | Difference Equations and Z Transforms | | Basic Formula of Fourier Transform | | The Finite Element Method- A practical Course G R Liu, S S Quek | | The Finite Element Method -An Introduction with Partial Differential Equations A. J. Davies | | Finite Element Method in Engineering Singiresu S.Rao | | A First Course in the Finite Element Method Daryl L. Logan | | A First Course in Finite Elements Jacob Fish, Ted Belytschko | | Power Plant Engineering P K Nag | | Power Plant Engineering A K Raja, Amit Prakash Srivastava, Manish Dwivedi | | Thermodynamic Cycles | | The Power of your Sub Conscious Mind Joseph Murphy, Ailish McGrath | | Safety Of Kudankulam Nuclear Power Plant | | Pressure Vessels - Easy Notes David Roylance | | Methods of Flow Measurement for Water and Waste water Riyaz Jiwani | | Fluid Mechanics- Laboratory Manual | | Fundamentals of Fluid Mechanics Munson, Young, Okiishi, Huebsch | | Industrial Flow Measurement - Seminar Slides David W. Spitzer | | Flow Measurement BJ Furman | | Eckhart Tolle A New Earth | | Conduction Heat Transfer - Notes Daniel W. Mackowski |