... of Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-5 21- 4 310 8-5)Copyright (C) 19 88 -19 92 by Cambridge University Press.Programs Copyright (C) 19 88 -19 92 ... of Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-5 21- 4 310 8-5)Copyright (C) 19 88 -19 92 by Cambridge University Press.Programs Copyright (C) 19 88 -19 92 ... IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-5 21- 4 310 8-5)Copyright (C) 19 88 -19 92 by Cambridge University Press.Programs Copyright (C) 19 88 -19 92 by Numerical Recipes Software. Permission is...
... IntroductionA set of linear algebraic equations looks like this:a 11 x 1 + a 12 x2+ a 13 x3+ ···+a1NxN=b 1 a 21 x 1 + a22x2+ a23x3+ ···+a2NxN=b2a 31 x 1 + a32x2+ a33x3+ ···+a3NxN=b3··· ... ···+a3NxN=b3··· ···aM1x 1 +aM2x2+aM3x3+···+aMNxN= bM(2.0 .1) Here the N unknowns xj, j =1, 2, ,N are related by M equations. Thecoefficients aijwith i =1, 2, ,M and j =1, 2, ,N are known ... is the right-hand side written as a column vector,A =a 11 a 12 a1Na 21 a22 a2N···aM1aM2 aMNb =b 1 b2···bM(2.0.3)By convention, the first index on an...
... following setof equations [1] :u= 998u + 19 98vv= −999u − 19 99v (16 .6 .1) with boundary conditionsu(0) = 1 v(0) = 0 (16 .6.2)By means of the transformationu =2y−zv=−y+z (16 .6.3)we find ... 734Chapter 16 . Integration of Ordinary Differential Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-5 21- 4 310 8-5)Copyright (C) 19 88 -19 92 by Cambridge ... =2e−x−e 10 00xv = −e−x+ e 10 00x (16 .6.4)If we integrated the system (16 .6 .1) with any of the methods given so far in thischapter, the presence of the e 10 00xterm would require a stepsize h 1/ 1000...