non linear partial differential equations with discrete state dependent delays in a metric space

... (19 .0.3) we substitute a finite-difference representation (see Figure 19 .0.2), uj +1, l − 2uj,l + uj 1, l uj,l +1 − 2uj,l + uj,l 1 + = ρj,l ∆2 ∆2 (19 .0.5) or equivalently uj +1, l + uj 1, l + uj,l +1 ... 1) + l for j = 0, 1, , J, l = 0, 1, , L (19 .0.7) In other words, i increases most rapidly along the columns representing y values Equation (19 .0.6) now becomes ui+L +1 + ui−(L +1)...

Ngày tải lên: 28/10/2013, 22:15

... differencing of equation (19.1 .20 ) is n+1 n rj+1 /2 − rj+1 /2 n+1 /2 sj n+1 /2 = ∆t n−1 /2 − sj =v ∆t n+1 /2 − sj ∆x n n rj+1 /2 − rj−1 /2 sj+1 (19.1.35) ∆x If you substitute equation (19.1 .22 ) in equation (19.1.35), ... (19.1.40) Then ξ = − iα sin k∆x − 2 (1 − cos k∆x) (19.1.41) so |ξ |2 = − 2 (1 − 2 )(1 − cos k∆x )2 (19.1. 42) The stability criterion |ξ |2 ≤ is therefore 2...

Ngày tải lên: 07/11/2013, 19:15

... Dividing by α, we see that the difference equations are just the finite-difference form of the equilibrium equation 850 Chapter 19 Partial Differential Equations t or n (a) x or j Fully Implicit ... (1 + iH∆t)−1 ψj ψj (19.2 .34 ) These are both first-order accurate in time, as can be seen by expanding equation (19.2 .32 ) However, neither operator in (19.2 .33 ) or (19.2 .34 ) is unitar...

Ngày tải lên: 15/12/2013, 04:15

... 8 54 Chapter 19 Partial Differential Equations Lax Method for a Flux-Conservative Equation As an example, we show how ... 1-800-872- 742 3 (North America only),or send email to trade@cup.cam.ac.uk (outside North America) − (cos kx∆ − cos ky ∆)2 − (αy sin kx ∆ − αx sin ky ∆)2 856 Chapter 19 Partial Differential Equations ... REFERENCES AND FURTHER READING: Ames, W.F 1977, Numerica...

Ngày tải lên: 15/12/2013, 04:15

... 858 Chapter 19 Partial Differential Equations Fourier Transform Method The discrete inverse Fourier transform in both ... waves: 860 Chapter 19 Partial Differential Equations If f(y = l∆) ≡ fl , then we get An from the inverse formula An = sinh πn L−1 fl sin l=1 πnl L (19.4.14) u = ujl + uH jl (19.4. 15) By adding appropriate ... North America) ∂u = g(y) ∂x 862 Chapter 19 Partial...

Ngày tải lên: 15/12/2013, 04:15

... problem for which ρJacobi is given by equation (19.5.11) Then equations (19.5.19) and (19.5.20) give 868 Chapter 19 Partial Differential Equations Consider a general second-order elliptic equation ... Chapter 19 Partial Differential Equations ADI (Alternating-Direction Implicit) Method The ADI method of §19.3 for diffusion equations can be turned into a relaxation method for e...

Ngày tải lên: 15/12/2013, 04:15

... http://www.nr.com or call 1-800- 872 -74 23 (North America only),or send email to trade@cup.cam.ac.uk (outside North America) S E 876 Chapter 19 Partial Differential Equations Its symbol is therefore ... fill0(double **u, int n); double disc,fact,h=0.5; 888 Chapter 19 Partial Differential Equations CITED REFERENCES AND FURTHER READING: Brandt, A 1 977 , Mathematics of Computation,...

Ngày tải lên: 24/12/2013, 12:16

... element A function p satisfying (1) and (2) is sometimes called a Minkowski functional H Brezis, Functional Analysis, Sobolev Spaces and Partial Differential Equations, DOI 10.1007/978-0-387-70914-7_1, ... Pick any x0 ∈ ω and r0 > such that B(x0 , r0 ) ⊂ ω Then, choose x1 ∈ B(x0 , r0 ) ∩ O1 and r1 > such that H Brezis, Functional Analysis, Sobolev Spaces and Pa...

Ngày tải lên: 04/02/2014, 11:10

... Galo, I Albarreal, M.C Calzada, J.L Cruz, E Fernandez-Cara, M Mari´n, Stability and Convergence of a Parallel ´ Fractional Step Method for the Solution of Linear Parabolic Problems, Applied Mathematics ... Marszalek, Z Trzaska, A Boundary-value Problem for Linear PDAEs, Int.J.Appl.Math.Comput.Sci., Vol 12, No (2002) 487 [3] T Lu, P Neittaanmaki, X.C Tai, A Parallel Split...

Ngày tải lên: 13/02/2014, 03:20

... Differential Equations with Linear Algebra This page intentionally left blank Differential Equations with Linear Algebra Matthew R Boelkins, J L Goldberg, and Merle C Potter 2009 Oxford ... blank Differential Equations with Linear Algebra This page intentionally left blank Essentials of linear algebra 1.1 Motivating problems The subjects of differential...

Ngày tải lên: 11/06/2014, 07:16

Ngày tải lên: 12/06/2014, 16:17

... manuscript No (will be inserted by the editor) Minimal and maximal solutions to first-order differential equations with state-dependent deviated arguments Rub´n Figueroa∗ and Rodrigo L´pez Pouso e o Department ... may have minimal (maximal) solutions between given lower and upper solutions and not have the least (greatest) solution This seems to be a peculiar fea...

Ngày tải lên: 20/06/2014, 20:20

... evolution equations, ” Journal of Evolution Equations, vol 3, no 2, pp 361–373, 2003 [10] W M Ruess, “Existence of solutions to partial functional evolution equations with delay,” in ´ Functional ... solutions to partial functional- differential equations with delay,” Advances in Differential Equations, vol 4, no 6, pp 843–876, 1999 Hassane Bouzahir 13 [12] W M Ruess, “...

Ngày tải lên: 22/06/2014, 22:20

... multi-point boundary value problem, Annali di Matematica Pura ed Ap[4] plicata Series IV 86 (1970), 367–399 [5] I Kiguradze, Some singular boundary value problems for ordinary differential equations, ... optimal conditions for the solvability of two-point singular boundary value problems, [6] Functional Differential Equations 10 (2003), no 1-2, 259–281, Functional differe...

Ngày tải lên: 23/06/2014, 00:20

... convergence of strong error of EM type approximation schemes for stochastic functional differential equations, e.g in [10], [13], [12], [1], [7], [8] for stochastic differential delay equations, ... functional differential equations with distributed memory term, Monte Carlo Methods Appl 3-4 (2004) 235-244 [3] E Buckwar, One-step approximations for stochastic...

Ngày tải lên: 14/10/2015, 07:55