linear ordinary differential equations solution

Ngày tải lên: 19/03/2015, 08:49

... Integration of Ordinary Differential Equations 16.0 Introduction Problems involving ordinary differential equations (ODEs) can always be reduced to the study of sets of first-order differential equations. ... 1973, Computational Methods in Ordinary Differential Equations (New York: Wiley). Lapidus, L., and Seinfeld, J. 1971, Numerical Solution of Ordinary Differential Equations (New York: Academic ... smooth in a solution, while your auxiliary variables are doing crazy things, then figure out why and choose different auxiliary variables. The generic problem in ordinary differential equations...

Ngày tải lên: 15/12/2013, 04:15

... 1973, Computational Methods in Ordinary Differential Equations (New York: Wiley). Lapidus, L., and Seinfeld, J. 1971, Numerical Solution of Ordinary Differential Equations (New York: Academic ... REFERENCES AND FURTHER READING: Gear, C.W. 1971, Numerical Initial Value Problems in Ordinary Differential Equations (Englewood Cliffs, NJ: Prentice-Hall). Acton, F.S. 1970, Numerical Methods ... 710 Chapter 16. Integration of Ordinary Differential Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN...

Ngày tải lên: 15/12/2013, 04:15

... 722 Chapter 16. Integration of Ordinary Differential Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN ... REFERENCES AND FURTHER READING: Gear, C.W. 1971, Numerical Initial Value Problems in Ordinary Differential Equations (Englewood Cliffs, NJ: Prentice-Hall). [1] Cash, J.R., and Karp, A.H. 1990, ACM ... ,n−1 y(x+H)≈y n ≡ 1 2 [z n +z n−1 +hf(x + H, z n )] (16.3.2) 714 Chapter 16. Integration of Ordinary Differential Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN...

Ngày tải lên: 24/12/2013, 12:16

... 722 Chapter 16. Integration of Ordinary Differential Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN ... REFERENCES AND FURTHER READING: Gear, C.W. 1971, Numerical Initial Value Problems in Ordinary Differential Equations (Englewood Cliffs, NJ: Prentice-Hall). [1] Cash, J.R., and Karp, A.H. 1990, ACM ... ofthe modied midpointmethod tothe Bulirsch-Stoertechnique (Đ16.4) derives from a deep result about equations (16.3.2), due to Gragg. It turns out that the error of (16.3.2), expressed as a power...

Ngày tải lên: 24/12/2013, 12:16

... quick-and-dirty, low-accuracy solution of a set of equations. A second warning is that the techniques in this section are not particularly good for differential equations that have singular points ... method, discussed in this section, is the best known way to obtain high-accuracy solutions to ordinary differential equations with minimal computational effort. (A possible exception, infrequently ... Method The techniques described in this section are not for differential equations containing nonsmooth functions. For example, you might have a differential equation whose right-handside involves a...

Ngày tải lên: 24/12/2013, 12:16

... Second-Order Conservative Equations Usually when you have a system of high-order differential equations to solve it is best to reformulate them as a system of rst-order equations, as discussed ... 27, pp. 505–535. 16.6 Stiff Sets of Equations As soon as one deals with more than one first-order differential equation, the possibility of a stiff set of equations arises. Stiffness occurs in ... reason for this is explained below). This is so even 732 Chapter 16. Integration of Ordinary Differential Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN...

Ngày tải lên: 24/12/2013, 12:16

... in fact the correct solution of the differential equation. If we think of x as representing time, then the implicit method converges to the true equilibriumsolution(i.e., the solution at late times) ... implicit methods holds only for linear systems, but even in the general case implicit methods give better stability. 742 Chapter 16. Integration of Ordinary Differential Equations Sample page from ... hf(y n+1 )(16.6.15) In general thisissome nasty set of nonlinear equationsthathasto be solvediteratively at each step. Suppose we try linearizing the equations, as in Newton’s method: y n+1 = y n + h  f(y n )+ ∂f ∂y     y n ·(y n+1 −...

Ngày tải lên: 24/12/2013, 12:16

... Problems in Ordinary Differential Equations (Englewood Cliffs, NJ: Prentice-Hall), Chapter 9. [1] Shampine, L.F., and Gordon, M.K. 1975, Computer Solution of Ordinary Differential Equations. The ... REFERENCES AND FURTHER READING: Gear, C.W. 1971, Numerical Initial Value Problems in Ordinary Differential Equations (Englewood Cliffs, NJ: Prentice-Hall). [1] Kaps, P., and Rentrop, P. 1979, Numerische ... Predictor-corrector methods have been, we think, squeezed 752 Chapter 16. Integration of Ordinary Differential Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN...

Ngày tải lên: 24/12/2013, 12:16

... conditions. Furthermore we consider linear equations, the Floquet theorem, and the autonomous linear flow. Then we establish the Frobenius method for linear equations in the com- plex domain and ... system. Moreover, if I = R, solutions exist for all t ∈ R by Theorem 2.12. Now observe that linear combinations of solutions are again solutions. Hence the set of all solutions forms a vector space. ... = x 0 is transformed into a linear system of equations by the Laplace transform. 3.3. General linear first order systems We begin with the study of the homogeneous linear first order system ˙x(t)...

Ngày tải lên: 31/03/2014, 15:56

... differential equations 11 3.1 Ordinary and partial differential equations 11 3.2 The order of a differential equation 13 3.3 Linear and nonlinear 13 3.4 Different types of solution 14 Exercises 16 4 ... a systematic way. 3.1 Ordinary and partial differential equations The most significant distinction is between ordinary and partial differential equa- tions, and this depends on whether ordinary or partial ... for nonlinear equations 89 10.1 Exact equations 89 10.2 Substitution methods 94 Exercises 97 Part II Second order linear equations with constant coefficients 99 11 Second order linear equations: ...

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