reduction to ordinary differential equations
an introduction to ordinary differential equations
Ngày tải lên :
12/05/2014, 03:24
... INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS This refreshing, introductory textbook covers standard techniques for solving ordinary differential equations, as well as introducing students to qualitative ... systematic way 3.1 Ordinary and partial differential equations The most significant distinction is between ordinary and partial differential equations, and this depends on whether ordinary or partial ... will consider only ordinary differential equations It is possible to write these two equations much more concisely using vector calculus notation Imagine that ∇ represents a vector of partial derivatives,...
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Báo cáo hóa học: " Research Article A Generalized Wirtinger’s Inequality with Applications to a Class of Ordinary Differential Equations" docx
Ngày tải lên :
22/06/2014, 02:20
... delay equations with three delays via bi-Hamiltonian ¸ systems,” Nonlinear Analysis: Theory, Methods & Applications, vol 64, no 11, pp 2433–2441, 2006 11 S Jekel and C Johnston, “A Hamiltonian ... delay differential equations, ” Journal of Differential Equations, vol 189, no 2, pp 396–411, 2003 R D Nussbaum, “A Hopf global bifurcation theorem for retarded functional differential equations, ” Transactions ... Society, vol 238, pp 139–164, 1978 J L Kaplan and J A Yorke, Ordinary differential equations which yield periodic solutions of differential delay equations, ” Journal of Mathematical Analysis and Applications,...
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Tài liệu Integration of Ordinary Differential Equations part 1 doc
Ngày tải lên :
15/12/2013, 04:15
... 16.6 of this chapter treats the subject of stiff equations, relevant both to ordinary differential equations and also to partial differential equations (Chapter 19) Sample page from NUMERICAL ... than Runge-Kutta In recent years Bulirsch-Stoer has been replacing predictor-corrector in many applications, but it is too soon to say that predictor-corrector is dominated in all cases However, ... sophisticated predictor-corrector routines are competitive Accordingly, we have chosen not to give an implementation of predictor-corrector in this book We discuss predictor-corrector further in §16.7,...
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Tài liệu Integration of Ordinary Differential Equations part 2 pptx
Ngày tải lên :
15/12/2013, 04:15
... yout[i]=y[i]+h6*(dydx[i]+dyt[i]+2.0*dym[i]); weights free_vector(yt,1,n); free_vector(dyt,1,n); free_vector(dym,1,n); 714 Chapter 16 Integration of Ordinary Differential Equations } CITED REFERENCES AND FURTHER ... along the trajectory of an ordinary differential equation can serve as an initial point The fact that all steps are treated identically also makes it easy to incorporate Runge-Kutta into relatively ... in mind, however, that the old workhorse’s last trip may well be to take you to the poorhouse: Bulirsch-Stoer or predictor-corrector methods can be very much more efficient for problems where very...
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Tài liệu Integration of Ordinary Differential Equations part 3 doc
Ngày tải lên :
24/12/2013, 12:16
... errmax,h,htemp,xnew,*yerr,*ytemp; 720 Chapter 16 Integration of Ordinary Differential Equations ak2=vector(1,n); ak3=vector(1,n); ak4=vector(1,n); ak5=vector(1,n); ak6=vector(1,n); ytemp=vector(1,n); for (i=1;i
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Tài liệu Integration of Ordinary Differential Equations part 4 ppt
Ngày tải lên :
24/12/2013, 12:16
... Chapter 16 Integration of Ordinary Differential Equations } CITED REFERENCES AND FURTHER READING: Gear, C.W 1971, Numerical Initial Value Problems in Ordinary Differential Equations (Englewood Cliffs, ... caveats, we believe that the Bulirsch-Stoer method, discussed in this section, is the best known way to obtain high-accuracy solutions to ordinary differential equations with minimal computational ... The usefulness of the modified midpoint method to the Bulirsch-Stoer technique (§16.4) derives from a “deep” result about equations (16.3.2), due to Gragg It turns out that the error of (16.3.2),...
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Tài liệu Integration of Ordinary Differential Equations part 5 pdf
Ngày tải lên :
24/12/2013, 12:16
... the Bulirsch-Stoer Method 729 d=matrix(1,nv,1,KMAXX); err=vector(1,KMAXX); x=vector(1,KMAXX); yerr=vector(1,nv); ysav=vector(1,nv); yseq=vector(1,nv); if (eps != epsold) { A new tolerance, so ... the extrapolation Safety factors Maximum factor for stepsize reduction Minimum factor for stepsize reduction Prevents division by zero 1/SCALMX is the maximum factor by which a stepsize can be ... 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 first-order equations, as discussed...
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Tài liệu Integration of Ordinary Differential Equations part 6 pdf
Ngày tải lên :
24/12/2013, 12:16
... not referenced Also input is htot, the total step to be taken, and nstep, the number of substeps to be used The output is returned as yout[1 nv], with the same storage arrangement as y derivs ... With this storage arrangement you can use bsstep simply by replacing the call to mmid with one to stoerm using the same arguments; just be sure that the argument nv of bsstep is set to 2n You ... (North America only),or send email to trade@cup.cam.ac.uk (outside North America) Then for k = 1, , m − 1, set 734 Chapter 16 Integration of Ordinary Differential Equations Note that for compatibility...
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Tài liệu Integration of Ordinary Differential Equations part 7 pptx
Ngày tải lên :
24/12/2013, 12:16
... free_vector(ysav,1,n); free_vector(g4,1,n); free_vector(g3,1,n); free_vector(g2,1,n); free_vector(g1,1,n); free_vector(err,1,n); free_vector(dysav,1,n); free_matrix(dfdy,1,n,1,n); free_vector(dfdx,1,n); free_matrix(a,1,n,1,n); ... Multivalue, and Predictor-Corrector Methods 747 free_vector(ysav,1,nv); free_vector(yerr,1,nv); free_vector(x,1,KMAXX); free_vector(err,1,KMAXX); free_matrix(dfdy,1,nv,1,nv); free_vector(dfdx,1,nv); ... Integration of Ordinary Differential Equations (1.0/2.0) (-3.0/2.0) (121.0/50.0) (29.0/250.0) 1.0 (3.0/5.0) indx=ivector(1,n); a=matrix(1,n,1,n); dfdx=vector(1,n); dfdy=matrix(1,n,1,n); dysav=vector(1,n);...
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Tài liệu Integration of Ordinary Differential Equations part 8 pdf
Ngày tải lên :
24/12/2013, 12:16
... that can be used to control accuracy and to adjust stepsize If one corrector step is good, aren’t many better? Why not use each corrector as an improved predictor and iterate to convergence on ... predictor-corrector approach using an explicit method for the predictor, or by Newton iteration for stiff systems Why go to all the trouble of introducing a whole new method that turns out to be ... Value Problems in Ordinary Differential Equations (Englewood Cliffs, NJ: Prentice-Hall), Chapter [1] Shampine, L.F., and Gordon, M.K 1975, Computer Solution of Ordinary Differential Equations The...
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Tài liệu AN INTRODUCTION TO PARTIAL DIFFERENTIAL EQUATIONS ppt
Ngày tải lên :
16/02/2014, 15:20
... blank AN INTRODUCTION TO PARTIAL DIFFERENTIAL EQUATIONS A complete introduction to partial differential equations, this textbook provides a rigorous yet accessible guide to students in mathematics, ... Classification 1.3 Differential operators and the superposition principle 1.4 Differential equations as mathematical models 1.5 Associated conditions 1.6 Simple examples 1.7 Exercises First-order equations ... functions is called a system of m equations 1.3 Differential operators and the superposition principle A function has to be k times differentiable in order to be a solution of an equation of...
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introduction to partial differential equations - a computational approach - a. tveito, r. winther
Ngày tải lên :
31/03/2014, 15:56
... differential equations into partial differential equations (PDEs) and ordinary differential equations (ODEs) PDEs involve partial derivatives, whereas ODEs only involve derivatives with respect to one ... adopt to such problems, even if these equations may be hard to handle by an analytical approach In Chapter 12 we give a brief introduction to the Fourier transform and its application to partial ... introduction to this topic must focus on methods suitable for computers But these methods often rely on deep analytical insight into the equations We must therefore take great care not to throw away...
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introduction to stochastic differential equations v1.2 (berkeley lecture notes) - l. evans
Ngày tải lên :
31/03/2014, 15:56
... familiarity with probability theory, measure theory, ordinary differential equations, and perhaps partial differential equations as well This is all too much to expect of undergrads But white noise, Brownian ... trajectories of systems modeled by (ODE) not in fact behave as predicted: X(t) x0 Sample path of the stochastic differential equation Hence it seems reasonable to modify (ODE), somehow to include ... Brownian motion and the random calculus are wonderful topics, too good for undergraduates to miss out on Therefore as an experiment I tried to design these lectures so that strong students could...
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ordinary differential equations and dynamical systems - g. teschl
Ngày tải lên :
31/03/2014, 15:56
... Introduction §1.1 Newton’s equations §1.2 Classification of differential equations §1.3 First order autonomous equations §1.4 Finding explicit solutions 11 §1.5 Qualitative analysis of first order equations ... Transform both equations into a first order system (ii) Compute the solution to the approximate system corresponding to the given initial condition Compute the time it takes for the stone to hit the ... differential equations into autonomous first order systems (i) x + t sin(x) = x ¨ ˙ (ii) x = − cos(t)x ¨ The last equation is linear Is the corresponding autonomous system also linear? 1.3 First order autonomous...
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introduction to stochastic differential equations 1.2 - evans l c
Ngày tải lên :
08/04/2014, 12:24
... familiarity with probability theory, measure theory, ordinary differential equations, and perhaps partial differential equations as well This is all too much to expect of undergrads But white noise, Brownian ... trajectories of systems modeled by (ODE) not in fact behave as predicted: X(t) x0 Sample path of the stochastic differential equation Hence it seems reasonable to modify (ODE), somehow to include ... Brownian motion and the random calculus are wonderful topics, too good for undergraduates to miss out on Therefore as an experiment I tried to design these lectures so that strong students could...
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báo cáo hóa học:" Research Article Variational Approach to Impulsive Differential Equations with Dirichlet Boundary Conditions" pptx
Ngày tải lên :
21/06/2014, 11:20
... differential equations, ” Journal of Mathematical Analysis and Applications, vol 318, no 2, pp 726–741, 2006 10 J J Nieto and D O’Regan, “Variational approach to impulsive differential equations, ” ... Chen, J J Nieto, and A Torres, “Analysis of a delayed epidemic model with pulse vaccination and saturation incidence,” Vaccine, vol 24, no 35-36, pp 6037–6045, 2006 J Li and J J Nieto, “Existence ... this paper, our aim is to study the existence of n distinct pairs of nontrivial solutions to the Dirichlet boundary problem for the second-order impulsive differential equations u t λh t, u t...
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Báo cáo hóa học: "TERMINAL VALUE PROBLEM FOR SINGULAR ORDINARY DIFFERENTIAL EQUATIONS: THEORETICAL ANALYSIS AND NUMERICAL SIMULATIONS OF GROUND STATES" pdf
Ngày tải lên :
22/06/2014, 22:20
... BVP [13] W Walter, Ordinary Differential Equations, Graduate Texts in Mathematics, vol 182, Springer, New York, 1998 [14] W Wasov, Asymptotic Expressions for Ordinary Differential Equations, John ... and free boundary problems for quasilinear elliptic operators, Advances in Differential Equations (2000), no 1–3, 1–30 [8] K Kuratowski, Topology II, Academic Press, New York, 1968 [9] P K Palamides, ... same time, to the methods of [9, 11] or [10] For the convenience of the reader and to make the paper self-contained, we summarize here the basic notions used in the sequel First, we refer to the...
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Numerical Methods for Ordinary Differential Equations Butcher Tableau doc
Ngày tải lên :
27/06/2014, 08:20
... correspond to incomplete eigenvector spaces and the need to use generalized eigenvectors Also, in this special case, the eigenvector corresponding to λ, together with the generalized eigenvectors if ... and Difference Equations 10 Differential Equation Problems 100 Introduction to differential equations As essential tools in scientific modelling, differential equations are familiar to every educated ... non-autonomous equation in an equivalent autonomous form All we need to to change the formulation is to introduce an additional component yN +1 into the y vector, and ensure that this can always maintain...
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Introduction to Partial Differential Equations: A Computational ApproachAslak Tveito Ragnar potx
Ngày tải lên :
29/06/2014, 16:20
... differential equations into partial differential equations (PDEs) and ordinary differential equations (ODEs) PDEs involve partial derivatives, whereas ODEs only involve derivatives with respect to one ... adopt to such problems, even if these equations may be hard to handle by an analytical approach In Chapter 12 we give a brief introduction to the Fourier transform and its application to partial ... introduction to this topic must focus on methods suitable for computers But these methods often rely on deep analytical insight into the equations We must therefore take great care not to throw away...
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