differential equations class 12 pdf

... Ordinary Differential Equations (Englewood Cliffs, NJ: Prentice-Hall), Đ 6.1.4. Stoer, J., and Bulirsch, R. 1980, Introduction to Numerical Analysis (New York: Springer-Verlag), Đ 7.2 .12. 16.4 ... 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 ... 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 inside...

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 ... is a 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 ... KMAXX =12in bsstep. CITED REFERENCES AND FURTHER READING: Deuflhard, P. 1985, SIAM Review , vol. 27, pp. 505–535. 16.6 Stiff Sets of Equations As soon as one deals with more than one first-order differential...

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 Initial ... 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

... matrices  a 11 a 12 a 21 a 22  and  c 11 c 12 c 21 c 22  (2.11.5) are inverses of each other. Then the c’s can be obtained from the a’s by the following operations (compare equations 2.7.22 ... 2.7.22 and 2.7.25): R 1 = Inverse(a 11 ) R 2 = a 21 ì R 1 R 3 = R 1 ì a 12 R 4 = a 21 ì R 3 R 5 = R 4 a 22 R 6 = Inverse(R 5 ) c 12 = R 3 ì R 6 c 21 = R 6 ì R 2 R 7 = R 3 ì c 21 c 11 = R 1 R 7 c 22 = ... 104 Chapter 2. Solution of Linear Algebraic Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5) Copyright...

Ngày tải lên: 24/12/2013, 12:16

Ngày tải lên: 23/06/2014, 00:20

Ngày tải lên: 21/07/2014, 20:22

Ngày tải lên: 21/07/2014, 20:22

... solutions of (4.4). OSCILLATION AND NONOSCILLATION THEOREMS FOR A CLASS OF EVEN-ORDER QUASILINEAR FUNCTIONAL DIFFERENTIAL EQUATIONS JELENA MANOJLOVI ´ C AND TOMOYUKI TANIGAWA Received 13 November ... Inequalities and Applications Volume 2006, Article ID 4 2120 , Pages 1–22 DOI 10.1155/JIA/2006/4 2120 8 Quasilinear functional differential equations Case 2. Let j ∈{0,1, ,n − 1} and suppose that ... theorems for a class of fourth order quasilinear func- tional differential equations, Hiroshima Mathematical Journal 33 (2003), no. 3, 297–316. [7] , Oscillation criteria for a class of higher...

Ngày tải lên: 22/06/2014, 21:20

... Exercises . . . . . 504 12 Regular Weak Taylor Approximations 507 12. 1 Weak Taylor Schemes . . 507 12. 2 Commutativity Conditions. . 514 12. 3 Convergence Results . . . 517 12. 4 Exercises . . . . ... Sydney PO Box 123 Broadway NSW 2007 Australia eckhard.platen@uts.edu.au Managing Editors Boris Rozovski ˘ ı Division of Applied Mathematics Brown University 182 George St Providence, RI 02 912 USA rozovsky@dam.brown.edu Geoffrey ... 978-3-642 -120 57-2 e-ISBN 978-3-642-13694-8 DOI 10.1007/978-3-642-13694-8 Springer Heidelberg Dordrecht London New York Library of Congress Control Number: 2010931518 Mathematics Subject Classication...

Ngày tải lên: 19/02/2014, 22:20

... formatted PDF and full text (HTML) versions will be made available soon. Lyapunov-type inequalities for a class of even-order differential equations Journal of Inequalities and Applications 2 012, 2 012: 5 ... differential equations. Commun. Pure Appl. Anal. 11(2), 465–473 (2 012) [19] Almansi, E: Sopra una delle esperienze di Plateau (Russian). Ann. Mat. Pura. Appl. 12, 1–17 (1905) 11 This Provisional PDF ... doi:10.1186/1029-242X-2 012- 5 Qi-Ming Zhang (zhqm20082008@sina.com) Xiaofei He (hexiaofei525@sina.com) ISSN 1029-242X Article type Research Submission date 19 October 2011 Acceptance date 12 January 2 012 Publication...

Ngày tải lên: 20/06/2014, 21:20

... pages doi:10.1155/2010/143298 Research Article On Connection between Second-Order Delay Differential Equations and Integrodifferential Equations with Delay Leonid Berezansky, 1 Josef Dibl ´ ık, 2, 3 and Zden ˘ ek ˇ Smarda 3 1 Department ... differential equations with damping described by 1.1. Despite the obvious importance in applications, there are only few papers on delay differential equations with damping. 4 Advances in Difference Equations a2 ... Difference Equations, vol. 2009, Article ID 671625, 15 pages, 2009. 7 N. V. Azbelev, V. P. Maksimov, and L. F. Rakhmatullina, Introduction to the Theory of Functional Differential Equations: ...

Ngày tải lên: 21/06/2014, 20:20

... differential equations, ” Journal of Differential Equations, vol. 189, no. 2, pp. 396–411, 2003. 2 R. D. Nussbaum, “A Hopf global bifurcation theorem for retarded functional differential equations, ” Transactions ... several delays,” Journal of Differential Equations, vol. 222, no. 2, pp. 425–438, 2006. 12 G. Fei, “Multiple periodic solutions of differential delay equations via Hamiltonian systems—I,” Nonlinear ... one-dimensional differential-delay equations, ” Tohoku Mathematical Journal, vol. 30, no. 1, pp. 13–35, 1978. 7 S. Chapin, “Periodic solutions of differential-delay equations with more than one delay,”...

Ngày tải lên: 22/06/2014, 02:20

... differential equations and some related perturbation results,” Annales Academiæ Scientiarium Fennicæ. Mathematica, vol. 27, no. 2, pp. 273–290, 2002. [9] E. Ince, Ordinary Differential Equations, ... Mathe- matical Society, vol. 21, no. 2, pp. 334–360, 1970. [12] S. A. Gao, Z. X. Chen, and T. W. Chen, The Complex Osc illation Theory of Linear Differential Equations, Middle China University of Technology ... = e z/q . Remark 4.3. Wiman-Valiron theory and its applications to differential equations (see [1, pages 5-6] or [12, pages 71-72]). Consider the linear differential equation a k f (k) + a k−1 f (k−1) +...

Ngày tải lên: 22/06/2014, 18:20

... functional-differential equations, ” Computers & Mathematic s with Applications, vol. 38, no. 11 -12, pp. 1–11, 1999. [4] D. D. Ba ˘ ınov and D. P. Mishev, Osc illation Theory for Neutral Differential Equations ... neutral differential equations, ” Dynamic Sys- tems and Applications, vol. 9, no. 3, pp. 353–360, 2000. [23] P. Wang and W. Shi, “Oscillatory theorems of a class of even-order neutral equations, ” Applied Mathematics ... 0 eventually for i = 0,1, ,n − 1. Now, using (2 .12) weget w (n) (t) −  b a w(t + τ − s) 1+α d s q 1 (t,s) −  d c w(t + τ + s) 1+α d s q 2 (t,s) ≥ 0. (2.14) 12 Journal of Inequalities and Applications where...

Ngày tải lên: 22/06/2014, 18:20

... equivalent to the system of the equations 2βp 12 =−1, p 11 + αp 12 + βp 22 = 0, 2p 12 +  2α + σ 2  p 22 =−1, (2.14) with the solution p 11 = α 2β − 1 −β 2α + σ 2 , p 12 =− 1 2β , p 22 = 1 −β β  2α ... the system of equations B 2 d 22 −d 11 = 0, B  d 12 + Ad 22  − d 12 = 0, d 11 +2Ad 12 + A 2 d 22 −d 22 =−1. (3.18) The solution of system (3.18)hastheform d 11 = B 2 d 22 , d 12 = AB 1 −B d 22 , d 22 =  1+B 1 ... Ad 22  B  d 12 + Ad 22  d 11 +2Ad 12 + A 2 d 22  . (3.17) RELIABILITY OF DIFFERENCE ANALOGUES TO PRESERVE STABILITY PROPERTIES OF STOCHASTIC VOLTERRA INTEGRO -DIFFERENTIAL EQUATIONS LEONID...

Ngày tải lên: 22/06/2014, 22:20

Ngày tải lên: 22/06/2014, 22:20

Ngày tải lên: 05/07/2014, 04:20

Ngày tải lên: 24/07/2014, 21:21

Ngày tải lên: 10/08/2014, 20:20

Ngày tải lên: 10/08/2014, 20:20