solving a system of ordinary differential equations using matlab

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Ngày tải lên: 21/06/2014, 03:20

... i.e., are not preserved automatically by the differential equations. Boundary conditionscan be as simple as requiring that certain variables have certain numerical values, or as complicated as a ... the original variables are 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 ... problem’s boundary conditions. Boundary conditions are algebraic conditions 707 710 Chapter 16. Integration of Ordinary Differential Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC...

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... Runge-Kuttamethod. Abramowitz and Stegun [1] , and Gear [2] , give various specific formulas that derive from this basic 712 Chapter 16. Integration of Ordinary Differential Equations Sample page from NUMERICAL ... the same accuracy. Is that so? The answer is: often, perhaps even usually, but surely not always! This takes us back to a central theme, namely that high order does not always mean high accuracy. ... (shown as a filled dot) is calculated. (See text for details.) contemporary practice of science rather than as a statement about strict mathematics. That is, it reflects thenatureofthe problems thatcontemporaryscientistsliketo...

Ngày tải lên: 15/12/2013, 04:15

... 1971, Numerical Initial Value Problems in Ordinary Differential Equations (Englewood Cliffs, NJ: Prentice-Hall), Chapter 2. [2] Shampine, L.F., and Watts, H .A. 1977, in Mathematical Software III , ... interestingand worthyof Gilbertand Sullivan’sMikado: The routinecan alwaysachieve an apparent zero error by making the stepsize so small that quantities of order hy  add to quantities of order y as if they ... vector() and matrix()). Because steps occur at unequal intervals results are only stored at intervals greater than dxsav.The top-level variable kmax indicates the maximum number of steps that can be...

Ngày tải lên: 24/12/2013, 12:16

... 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 Transactions ... A. H. 1990, ACM Transactions on Mathematical Software , vol. 16, pp. 201– 222. [2] Shampine, L.F., and Watts, H .A. 1977, in Mathematical Software III , J.R. Rice, ed. (New York: Academic Press), pp. ... trade@cup.cam.ac.uk (outside North America). Here the z’s are intermediate approximations which march along in steps of h, while y n is the final approximation to y(x + H). The method is basically...

Ngày tải lên: 24/12/2013, 12:16

... integration. The idea is to consider the final answer of a numerical calculation as itself being an analytic function (if a complicated one) of an adjustable parameter like the stepsize h.That analytic ... rather than to an arbitrary value. However, it is more complicated in that it must individually extrapolate each component of a vector of quantities. 728 Chapter 16. Integration of Ordinary Differential ... integrations allows a tableau like thatin Đ3.1 to be extended by one additional set of diagonals. The size of the new correction added at each stage is taken as the (conservative) error estimate. How...

Ngày tải lên: 24/12/2013, 12:16

... (North America only),or send email to trade@cup.cam.ac.uk (outside North America). Note that for compatibility with bsstep the arrays y and d2y are of length 2n for a system of n second-order equations. ... 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 in ... There 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...

Ngày tải lên: 24/12/2013, 12:16

... (North America only),or send email to trade@cup.cam.ac.uk (outside North America). Note that for compatibility with bsstep the arrays y and d2y are of length 2n for a system of n second-order equations. ... guaranteed to be stable, but it usually is, because the behavior is locally similar to the case of a constant matrix C described above. So far we have dealt only with implicit methods that are ... is stable for all stepsizes h. The penalty we pay for this stability is that we are required to invert a matrix at each step. Not all equations are linear with constant coefficients, unfortunately!...

Ngày tải lên: 24/12/2013, 12:16

... them, and there are a lot of standard ODE programs around that are based on predictor-corrector methods. Many capable researchers have a lot of experience with predictor-corrector routines, and ... no reason to make a precipitous change of habit. It is not a bad idea for you to be familiar with the principles involved, and even with the sorts of bookkeeping details that are the bane of these ... Francisco: W.H Freeman). [2] Acton, F.S. 1970, Numerical Methods That Work ; 1990, corrected edition (Washington: Mathe- matical Association of America), Chapter 5. Kahaner, D., Moler, C., and...

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Ngày tải lên: 19/03/2015, 08:49

... Briscoe, Ann Copes- take and Valeria de Paiva eds. Cambridge Uni- versity Press, Cambridge. Daelemans, Walter, Koenraad De Smedt and Ger- ald Gazdar. 1992. Inheritance in Natural Lan- guage Processing. ... a single value. Moreover, default specifications can be made to act as indefeasible information, using YADU's DefFill operation (Las- carides and Copestake, 1999), that has a TDFS as ... Briscoe, Ann Copestake and Valeria de Paiva eds. Cambridge University Press, Cambridge. Lascarides, Alex, Ann Copestake and Ted Briscoe. 199 6a. Ambiguity and Coherence. Journal of Semantics,...

Ngày tải lên: 17/03/2014, 23:20

... E 2 are locally asymptotically stable and E 3 is a saddle. There exists the global stable manifold W s (E 3 ) that separates the positive quadrant so that all orbits below this manifold are attracted ... 〚u 1 ,u 2 〛 other than u 1 and u 2 , then the interior of 〚u 1 ,u 2 〛 is either a subset of the basin of attraction of u 1 or a subset of the basin of attraction of u 2 . Kalabušić et al. Advances in Difference ... Island, Kingston, RI 02881-0816, USA Full list of author information is available at the end of the article Abstract We investigate global dynamics of the following systems of difference equations ⎧ ⎪ ⎨ ⎪ ⎩ x n+1 = α 1 + β 1 x n A 1 +...

Ngày tải lên: 21/06/2014, 00:20

... problem for a system of elliptic equations that strongly degenerate at a point Stasys Rutkauskas Correspondence: stasys. rutkauskas@mii.vu.lt Institute of Mathematics and Informatics of Vilnius ... University, Akademijos str. 4, LT-08863, Vilnius, Lithuania Abstract A system of elliptic equations which are irregularly degenerate at an inner point is considered in this article. The equations are weakly ... class of elliptic systems degenerating at an inner point. Math Model Anal. 6(1), 147–155 (2001) 6. Rutkauskas, S: On the Dirichlet problem for a system of degenerate at a point elliptic equations...

Ngày tải lên: 21/06/2014, 00:20

... and polynomial decay for a quasilinear viscoelastic problem. Nonlinear Anal. 68, 785–793 (2007) 8. Messaoudi, SA: General decay of solutions of a viscoelastic equation. J. Math. Anal. Appl. 341, ... Messaoudi, SA, Said-Houari, B: Global nonexistence of positive initial-energy solutions of a system of nonlinear viscoelastic wave equations with damping and source terms. J. Math. Anal. Appl. ... Simulation of Large Scale Complex Systems, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210046, PR China Full list of author information is available at the end of the article Abstract In...

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