... MethodThe 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 solutionof a set of equations. A second warning is that the techniques in this section arenot particularly good for differentialequations that have singular points inside ... method,discussed in this section, is the best known way to obtain high-accuracy solutions to ordinary differentialequations with minimal computational effort. (A possibleexception, infrequently...
... Second-Order Conservative Equations Usually when you have a system of high-order differentialequations to solve it is bestto reformulate them as a system of rst-order equations, as discussed ... 27, pp. 505–535.16.6 Stiff Sets of Equations As soon as one deals with more than one first-order differential equation, thepossibility of a stiff set of equations arises. Stiffness occurs in ... isa particular class of equations that occurs quite frequently in practice where you can gainabout a factor of two in efficiency by differencing the equations directly. The equations aresecond-order...
... Problems in Ordinary Differential Equations (EnglewoodCliffs, 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 (EnglewoodCliffs, NJ: Prentice-Hall). [1]Kaps, P., and Rentrop, P. 1979,Numerische ... Predictor-corrector methods have been, we think, squeezed 752Chapter 16. Integration of Ordinary Differential Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN...
... hardware devices and seems to provide solutions where no alternative is known.The focus of this book is on the numerical solution of stochastic differential equations (SDEs) with jumps via simulation ... abook to follow on the book with Peter Kloeden on the “Numerical Solution ofStochastic Differential Equations , which first appeared in 1992 at SpringerVerlag and helped to develop the theory and ... Webber (1995). Models for the dy-namics of financial quantities specified by stochastic differential equations (SDEs) with jumps have become increasingly popular. Models of this kindcan be found,...
... our existence theorem of solutions. 1 IntroductionAbstract measure differential equations are more general than difference equations, differential equations, and differential equations with impulses. ... solutions for abstract measure functional differential equations. There were some consideration on abstract measure delay differential equations [2] and perturbed abstractmeasure differential equations ... measuredifferential equations can be found, such as existence [2–6], uniqueness [2, 3, 5], and extremal solutions [3,4, 6]. There were also several researches on abstract measure integro-differential equations...
... thegrowth of meromorphic solutions of algebraic differential equations. Acta Math. Sci. This Provisional PDF corresponds to the article as it appeared upon acceptance. Fully formatted PDF and full text ... soon.Further results of the estimate of growth of entire solutions of some classes ofalgebraic differential equations Advances in Difference Equations 2012, 2012:6 doi:10.1186/1687-1847-2012-6Oi ... algebraic differential equations. Bull. HongKong Math. Soc. 2(1), 159–164 (1998)[8] Bergweiler, W: On a theorem of Gol’dberg concerning meromorphic solutions ofalgebraic differential equations. Complex...
... appeared upon acceptance. Fully formatted PDF and full text (HTML) versions will be made available soon.Minimal and maximal solutions to first-order differentialequations withstate-dependent deviated ... (11) has the extremal solutions in [α, β].Proof. Theorem 1 guarantees that problem (11) has a nonempty set of solutions between α and β. We will show that this set of solutions is, in fact,a ... is true for maximal and greatest solutions. Interestingly, we will show that problem (1) may have minimal (ma-ximal) solutions between given lower and upper solutions and not havethe least...
... Advances in Difference Equations 2011, 2011:58http://www.advancesindifferenceequations.com/content/2011/1/58Page 3 of 12 RESEARCH Open AccessPolynomial solutions of differential equations H Azad*, ... ArabiaAbstractA new approach for investigating polynomial solutions of differentialequations isproposed. It is based on elementary linear algebra. Any differential operator of theformL(y)=k=Nk=0ak(x)y(k), ... polynomial solutions of a class of linear differentialequations of the second order. Bull A M S. 36,77–84 (1930). doi:10.1090/S0002-9904-1930-04888-0Azad et al. Advances in Difference Equations...
... fractional differential equations. NonlinearAnal 2010, 72:1604-1615.32. Agarwal RP, O’Regan D, Stanek S: Positive solutions for Dirichlet problems of singular nonlinear fractional differential equations. ... problem for non-linear differential equations of fractional order. Nonlinear Anal 2011, 74:792-804.34. Zhang L, Wang G: Existence of solutions for nonlinear fractional differentialequations with impulses ... Wang et al.: Positive solutions of the three-point boundary value problem for fractional-order differential equations with an advanced argument. Advances in Difference Equations 2011 2011:2.Submit...
... Kilbas AA, Trujillo JJ: Differentialequations of fractional order: methods, results and problem. I Appl Anal 2001,78:153-192.6. Kilbas AA, Trujillo JJ: Differentialequations of fractional ... value problem of fractional differential equations. J Univ Jinan 2010, 24:312-315.Zhao et al. Advances in Difference Equations 2011, 2011:10http://www.advancesindifferenceequations.com/content/2011/1/10Page ... for singular fractional equations. Electron J Differ Equ 2008, 146:1-9.15. Zhang S: Positive solutions for boundary-value problems of nonlinear fractional differential equations. Electron JDiffer...