applications of ordinary differential equations ppt

... 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 ... 710 Chapter 16. Integration of Ordinary Differential Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5) Copyright ... that derive from this basic 712 Chapter 16. Integration of Ordinary Differential Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5) Copyright...

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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 0-521-43108-5) Copyright ... Initial Value Problems in Ordinary Differential Equations (Englewood Cliffs, NJ: Prentice-Hall). [1] Cash, J.R., and Karp, A.H. 1990, ACM Transactions on Mathematical Software , vol. 16, pp. 201– 222. ... modified midpoint method, which advances a vector of dependent variables y(x) from a point x to a point x + H by a sequence of n substeps each of size h, h = H/n (16.3.1) In principle, one could...

Ngày tải lên: 24/12/2013, 12:16

... form of the midpoint rule: y n+1 − y n−1 =2hf  y n+1 + y n−1 2  (16.6.29) 738 Chapter 16. Integration of Ordinary Differential Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC ... intermediate values of y and x. y[i]=ysav[i]+A31*g1[i]+A32*g2[i]; 736 Chapter 16. Integration of Ordinary Differential Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING ... vol. 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...

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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...

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 0-521-43108-5) Copyright ... ,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 0-521-43108-5) Copyright ... informationcan beobtained. Obviously, 720 Chapter 16. Integration of Ordinary Differential Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5) Copyright...

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... extrapolate each component of a vector of quantities. 728 Chapter 16. Integration of Ordinary Differential Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN ... method a degree of robustness for problems with discontinuities. Let us remind you once again that scaling of the variables is often crucial for successful integration of differential equations. The ... differential equations. For n k subdivisions in H, the number of function evaluations can be found from the recurrence A 1 = n 1 +1 A k+1 = A k + n k+1 (16.4.6) 730 Chapter 16. Integration of Ordinary Differential...

Ngày tải lên: 24/12/2013, 12:16

... vol. 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 ... 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 ... 734 Chapter 16. Integration of Ordinary Differential 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

... adjusting the stepsize is difficult. 748 Chapter 16. Integration of Ordinary Differential Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5) Copyright ... 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 0-521-43108-5) Copyright ... number of iterations in advance, then the final valueof y n+1 can be writtenas somecomplicated functionofknownquantities. Thus fixed iteration PC methods lose the strong stability properties of implicit...

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... The trunk of the tree denotes the joint forces of scientists from different branches of study in the development of a wavelet theory. The branches are the different directions and applications which ... varied the concept of the transform. Instead of keeping the size of the window fixed and filling it with oscillations of different frequencies, he tried the reverse: He kept the number of oscillations ... transform onagrid[Hol95] ề ắ ềắ à ề ắ ể IV K URZFASSUNG LIST OF FIGURES XIX 6.17 Two examples of a pre–defined shape of a region of interest 112 6.18 Region of interest mask with three quality levels 113 7.1...

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... for example, in three of the four quadrants of the i-v characteristic and can therefore act as sources of energy for specific combinations of voltages and currents. An example of this dual behavior ... one of Kirchhoff’s laws results in a single equation, while the other results in two equations. In Chapter 3 we shall develop methods for systematically writing the smallest possible number of equations ... resistance of value R EQ , where R EQ = R 1 + R 2 + R 3 The three resistors could thus be replaced by a single resistor of value R EQ without changing the amount of current required of the battery....

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... Canonical form of parabolic equations 69 3.5 Canonical form of elliptic equations 70 3.6 Exercises 73 vii 1.4 Differential equations as mathematical models 13 1.4.4 Random motion Random motion of minute ... semilinear. r Scalar equations versus systems of equations A single PDE with just one unknown function is called a scalar equation. In contrast, a set of m equations with l unknown functions is called a system of ... conditions such as initial conditions (as we have of- ten seen in the theory of ordinary differential equations (ODEs)) or boundary conditions. The analysis of PDEs has many facets. The classical approach...

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... find the general solution of the differential equation. Chapter 0 Ordinary Differential Equations 3 Principle of Superposition. If u 1 (t) and u 2 (t) are solutions of the same linear homogeneous ... be supplied by the lower part of the column. 34 Chapter 0 Ordinary Differential Equations multiple of π ,sincesin(π ) = 0, sin(2π) = 0, etc., and integer multiples of π are the only arguments ... 32 Chapter 0 Ordinary Differential Equations Figure 7 Column carrying load P. Figure 8 Section of column showing forces and moments. been of second order, causing the appearance of two arbitrary...

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