first order linear ordinary differential equations examples

... nonlinear first order ordinary differential equations. Math Inequal Appl. 6, 477–485 (2003) 23. Luo, ZG, Shen, JH, Nieto, JJ: Antiperiodic boundary value problem for first -order impulsive ordinary ... following first- order nonlinear integro -differential system with periodic boundary value conditions.  x  = f (t, x,(Kx)(t )), t ∈ [0 , 1] ; x(0) = x(1); (1:1) and first- order integro -differential ... Difference Equations 2011, 2011:14 http://www.advancesindifferenceequations.com/content/2011/1/14 Page 14 of 17 RESEARCH Open Access Some new results for BVPs of first- order nonlinear integro-differential...

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... second -order superlinear neutral differential equations. Math Slovaca. (to appear) 12. Li, T, Han, Z, Zhang, C, Li, H: Oscillation criteria for second -order superlinear neutral differential equations. ... even -order neutral delay differential equations. Adv Differ Equ. 2010,1–9 (2010) 14. Li, T, Thandapani, E: Oscillation of solutions to odd -order nonlinear neutral functional differential equations. ... non -linear neutral delay differential equations of higher order for p(t) = ± 1. Arch Math. 40, 359–366 (2004) 16. Tang, S, Li, T, Thandapani, E: Oscillation of higher -order half -linear neutral differential...

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... 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. ... auxiliary variables. The generic problem in ordinary differential equations is thus reduced to the study of a set of N coupled first -order differential equations for the functions y i ,i=1,2, ,N, ... 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...

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... 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 ... all agree to first order, but that have different coefficients of higher -order error terms. Adding up the right combination of these, we can eliminate the error terms order by order. That is the ... 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...

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... 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 ... a second -order method, like (16.1.2), but with the advantage of requiring(asymptoticallyfor large n) only one derivative evaluation per step h instead of the two required by second -order Runge-Kutta....

Ngày tải lên: 24/12/2013, 12:16

... solutions to ordinary differential equations with minimal computational effort. (A possible exception, infrequently encountered in practice, is discussed in Đ16.7.) 726 Chapter 16. Integration of Ordinary ... REFERENCES AND FURTHER READING: Gear, C.W. 1971, Numerical Initial Value Problems in Ordinary Differential Equations (Englewood Cliffs, NJ: Prentice-Hall), Đ 6.1.4. Stoer, J., and Bulirsch, R. ... 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...

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... [3] 16.5 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 ... particular class of equations that occurs quite frequently in practice where you can gain about a factor of two in efficiency by differencing the equations directly. The equations are second -order systems...

Ngày tải lên: 24/12/2013, 12:16

... 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 − ... 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...

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... 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 ... stepsize would be predicted using an order one greater and one smaller than the current order. Choose the order that allows you to take the biggest next step. Being able to change order also allows an easy ... 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

... 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) = A(t)x(t), ... 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 ... = 1 2πi  |z|=1 dz z − A(λ) , P − (A(λ)) = I − P + (A(λ)).) 3.2. Linear autonomous first order systems We now turn to the autonomous linear first order system ˙x = Ax. (3.34) 5.3. Regular Sturm-Liouville...

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... 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: ... 9 3 Classification of 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 ... 242 Exercises 245 Part V Coupled linear equations 247 25 *Vector first order equations and higher order equations 249 25.1 Existence and uniqueness for second order equations 251 Exercises 252 26...

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... third -order differential equations see 1–20. Various techniques appeared for the investigation of such equations. Some of them 1, 19 make use of the methods developed for the second -order equations ... Corporation Advances in Difference Equations Volume 2010, Article ID 160761, 12 pages doi:10.1155/2010/160761 Research Article Comparison Theorems for the Third -Order Delay Trinomial Differential Equations B. Bacul ´ ıkov ´ aandJ.D ˇ zurina Department ... equations of third order, ” Nonlinear Analysis: Theory, Methods & Applications, vol. 34, no. 3, pp. 391–403, 1998. 14 N. Parhi and S. Padhi, “Asymptotic behaviour of solutions of third order...

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... Difference Equations Volume 2009, Article ID 143175, 14 pages doi:10.1155/2009/143175 Research Article On the Spectrum of Almost Periodic Solution of Second -Order Neutral Delay Differential Equations with ... 14 Advances in Difference Equations 12 R. Yuan, “On the spectrum of almost periodic solution of second -order differential equations with piecewise constant argument,” Nonlinear Analysis: Theory, ... Advances in Difference Equations 5 Suppose that |p| /  1. First, multiply the two sides of 2.3 and 2.4 by p and 2p − 1, respectively, then add the resulting equations to get x 2n1  1 2p...

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