euler s forward time and backward space ftbs approximations first order upwind scheme
computational fluid dynamics, second edition
... various solution schemes for compressible flows are presented Potential equations, Euler equations, and the Navier-Stokes system of equations are included Central schemes, first order and second order ... 6.2.6 Second Order Upwind Schemes with High Resolution (TVD Schemes) 6.2.7 Essentially Nonoscillatory Scheme 6.2.8 Flux-Corrected Transport Schemes 6.3 Navier-Stokes System of Equations 6.3.1 ... Schemes with Independent Space -Time Discretization 6.2.4 First Order Upwind Schemes 6.2.4.1 Flux Vector Splitting Method 6.2.4.2 Godunov Methods 6.2.5 Second Order Upwind Schemes with Low Resolution...
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Báo cáo toán học: " Minimal and maximal solutions to first-order differential equations with state-dependent deviated arguments" pptx
... main results in this article, which are two existence results for problem (1) between given lower and upper solutions The first result ensures the existence of maximal and minimal solutions, and ... and the second one establishes the existence of the greatest and the least solutions in a particular case The concepts of lower and upper solutions introduced in Section are new, and we show with ... interests The authors declare that they have no competing interests Authors’ contributions Both authors’ contributions to this paper are similar and it is impossible to say which part corresponds...
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báo cáo hóa học:" Research Article Nonoscillation of First-Order Dynamic Equations with Several Delays" pdf
... on Time Scales An Introduction with Applications, Birkh¨ user Boston, Boston, Mass, USA, 2001 a B Karpuz, “Existence and uniqueness of solutions to systems of delay dynamic equations on time scales,” ... introduced Section contains a nonoscillation criterion which is the main result of the present paper Section presents comparison theorems All results are illustrated by examples on “nonstandard” time scales ... time- scale calculus Let us now present some oscillation and nonoscillation results on delay dynamic equations, and from now on, we will without further more mentioning suppose that the time scale...
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STABILITY OF PERIODIC SOLUTIONS OF FIRST-ORDER DIFFERENCE EQUATIONS LYING BETWEEN LOWER AND UPPER pptx
... set of solutions of (PN ) is closed and well ordered, we conclude that uS is a solution of problem (PN ) If uS is isolated from below, it is clear that uS ∈ C, and so it is asymptotically stable ... constant solutions are stables from above and solution is asymptotically stable from below Given that is not isolated in the set of constant solutions of this problem, it is not asymptotically stable ... lower solutions (yn < T yn in JN ) and a strictly decreasing sequence of strict upper solutions (Tzn < zn in JN ); that is, it is a strongly order- stable fixed point of T (see [5]) Thus we may assert...
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báo cáo hóa học: " Some new results for BVPs of first-order nonlinear integro-differential equations of volterra type" doc
... find two constants R >0 and a ≥ satisfying (2.12) and (2.13) at the same time Existence results for “non-periodic” conditions In this section we study the problem of existence of solutions for BVP ... f (s, x (s) , (Kx) (s) )ds − (A + B) Tx(t) = (3:3) f (s, x (s) , (Kx) (s) )ds, t ∈ [0, 1] B Since f is continuous, we see that T is also a continuous map It is easy to verify that the operator T is compact ... presents some existence theorems for PVPs (1.1), (1.3) and a couple of examples to illustrate how our newly developed results work In Sect we focus on the existence of solutions for (1.2) and...
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báo cáo hóa học:" Periodic boundary value problems for nonlinear first-order impulsive dynamic equations on time scales" pot
... address: wangdb@lut.cn Abstract By using the classical fixed point theorem for operators on cone, in this article, some results of one and two positive solutions to a class of nonlinear first -order ... Peterson, A: Advances in Dynamic Equations on Time Scales Birkhauser, Boston (2003) [21] Hilger, S: Analysis on measure chains-a unified approach to continuous and discrete calculus Results Math ... JL, Shen, JH: Existence results for second -order impulsive boundary value problems on time scales Nonlinear Anal 70, 1648–1655 (2009) [31] Li, YK, Shu, JY: Multiple positive solutions for first-order...
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Báo cáo hóa học: " Research Article First-Order Singular and Discontinuous Differential Equations" docx
... Equations with Discontinuous Righthand Sides, vol 18 of Mathematics and Its Applications (Soviet Series), Kluwer Academic Publishers, Dordrecht, The Netherlands, 1988 11 S Heikkil¨ and V Lakshmikantham, ... of the solutions In Section we prove two existence results in case f does not have such a strong bound as in Section singular problems , which requires the addition of some assumptions over the ... continuous cases e Discontinuous Lower and Upper Solutions Another modification of the concepts of lower and upper solutions concerns the possibility of allowing jumps in their graphs Since the task...
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Báo cáo hoa học: " Research Article Multiple Positive Solutions for Nonlinear First-Order Impulsive Dynamic Equations on Time Scales with Parameter" ppt
... Equations on Time Scales: An Introduction with Applications, Birkh¨ user, Boston, Mass, USA, 2001 a M Bohner and A Peterson, Eds., Advances in Dynamic Equations on Time Scales, Birkh¨ user, Boston, ... Mass, USA, 2003 S Hilger, “Analysis on measure chains-a unified approach to continuous and discrete calculus,” Results in Mathematics, vol 18, no 1-2, pp 18–56, 1990 V Lakshmikantham, S Sivasundaram, ... Systems with Impulse Effect: Stability, Theory and Applications, Ellis ı Horwood Series: Mathematics and Its Applications, Ellis Horwood, Chichester, UK, 1989 D D Bainov and P S Simeonov, Impulsive...
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Báo cáo hóa học: " Research Article Maximum Principles and Boundary Value Problems for First-Order Neutral Functional Differential Equations" potx
... decrease This allows us to obtain various results about existence and uniqueness of solutions of boundary value problems for these equations without the standard assumption about smallness of ... equations is essentially based on the questions of the action and estimates of the spectral radii of the operators in the spaces of discontinuous functions, for example, in the spaces of summable ... formulas s, ∞ s, ∞ t t As x t x ξ dξ a t, ξ , Bs x t s x ξ dξ b t, ξ , t ∈ s, ∞ , and the operator Ss : L∞ → L∞ is defined by the equality Ss ys t s, ∞ s, ∞ y t for t ≥ s and y t for t < s We have ys t...
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Báo cáo hóa học: " Research Article Iterated Oscillation Criteria for Delay Dynamic Equations of First Order" pdf
... Equations 10 Y Sahiner and I P Stavroulakis, “Oscillations of first order delay dynamic equations,” Dynamic ¸ Systems and Applications, vol 15, no 3-4, pp 645–655, 2006 11 M Bohner and A Peterson, ... q > and τ ∈ N This time Example 3.3 Let T qN0 : {qn : n ∈ N0 } and τ t scale is different than the well-known time scales R and Z since t s/ T for t, s ∈ T In the ∈ present case, 3.1 reduces to ... Equations on Time Scales: An Introduction with Application, Birkh¨ user, Boston, Mass, USA, 2001 a 12 Advances in Difference Equations 12 M Bohner and A Peterso, Eds., Advances in Dynamic Equations...
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Báo cáo hóa học: "OSCILLATION CRITERIA FOR FIRST-ORDER FORCED NONLINEAR DIFFERENCE EQUATIONS" ppt
... numbers and τ is any real number In Section 3, we investigate the oscillatory property of (1.2) and discuss the case when λ = 1, that is, the linear case Section is devoted to the study of the oscillatory ... the referees for their suggestions on the first draft of this paper 16 Discrete first -order forced oscillation References [1] R P Agarwal, M Bohner, S R Grace, and D O’Regan, Discrete Oscillation ... that the results of this paper are presented in a form which is essentially new and of high degree of generality Also, for related results in oscillation of forced differential equations, we refer...
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FIRST- AND SECOND-ORDER DYNAMIC EQUATIONS WITH IMPULSE F. M. ATICI AND D. C. BILES Received 3 pdf
... medicine, physics, economics, pharmacokinetics, and engineering In this paper, we consider fixedtime impulses Without loss of generality, we investigate systems with a single impulse First order Let ... s, p s, u (s) s = u(t) − p 0,u(0) = u t2 − p 0,u(0) + u(t) − u t2 , t2 g s, p s, u (s) s + u(t) − u t2 = u(t) − u t2 = ⇒ = t t2 t g s, p s, u (s) s − t2 g s, p s, u (s) s = t2 (2.11) g s, p s, u (s) ... impulse, Proceedings of the Third Mississippi State Conference on Difference Equations and Computational Simulations (Mississippi, 1997), Electron J Differ Equ Conf., vol 1, Southwest Texas State...
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Đề tài " Sharp local wellposedness results for the nonlinear wave equation " pot
... DANIEL TATARU is well-posed in H × L2 , and its solution satisfies the energy estimates It remains to show that its solution v also satisfies the Strichartz estimates (3.3) Without loss of generality ... be established in subsequent sections is the following: Proposition 3.1 Suppose (1.7) holds Assume that the data (u0 , u1 ) is smooth, supported in B(0, c + 2), and satisfies u0 Hs + u1 H s 1 ... estimates are 296 HART F SMITH AND DANIEL TATARU established provided that the coefficients satisfy d2 g ∈ L1 L∞ As a byproduct, t x this last estimates implies Strichartz estimates with a loss...
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Đề tài " Propagation of singularities for the wave equation on manifolds with corners " ppt
... subset of those of Lebeau s However, since the analysis of bicharacteristics is local in X, the C ∞ boundary analysis of Melrose and Sj¨strand o applies As this only necessitates trivial changes, ... both sides are the standard wave front set, WFm+1 (u), so it suffices to consider the case when q lies over ∂X First we show that the left-hand side is a subset of the right-hand side, which is the ... of singularities in Section is standard, essentially due to Melrose and Sj¨strand [14, §3] Indeed, as presented by Lebeau [11, o Prop VII.1], basically no changes are necessary at all in this...
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Báo cáo khoa học: "EXPRESSING DISJUNCTIVE AND NEGATIVE FEATURE CONSTRAINTS CLASSICAL FIRST-ORDER LOGIC" pdf
... constraints) Table sketches some of the variety of feature structure models and constraint types that previous analyses have used This paper follows Kasper and Rounds and most proposals listed ... in which feature structure constraints are expressed and the structures that satisfy these constraints Unification is supplanted by conjunction of constraints, and disjunction and negation appear ... values to be used as attributes (although it would be easy to this) The soundness and completeness proofs in [9] and other papers listed in Table are not required here because these results are...
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a hierarchical classification of first-order
... ρ is denoted by inf(ρ) Besides, a cycle in A consists of a finite set of states c such that there exists a finite path in A with same origin and ending state that visits precisely all the sates ... tree) is a sequence of cycles of A (Ck,l )i≤p,j
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Solutions to the Acoustic Wave Acoustic Wave Equation
... P = Acos(wt) Time (s) w=2pi/T Period T = sec/cycle 1/T=f = cycle /s 2pi/T=w=radians /s Phase Time (s) Harmonic Ripples: P = Acos(kx) Wavenumber k=2pi/ Wavelength x Plane Wave Solution Faster Velocities ... v/sinO v/sinO=v x= z = O=90 Time (s) Examples: dx/dt = v/sinO x z = = O=0 = 0.0 Time (s) 0.45 0.0 X (ft) 250 Outline Plane Wave: Dispersion relationship, freq., wavelength, wavenumber, slowness, ... + z r is distance between pt source and observer at (x,y,z) Outline Plane Wave: Dispersion relationship, freq., wavelength, wavenumber, slowness, apparent velocity, apparent wavelength Spherical...
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Báo cáo sinh học: " Periodic solutions for a class of higher order difference equations" potx
... positive constants, τ : Z → Z and τ (n + ω) = τ (n), ω, m, k ∈ N, and obtained existence theorem for single and multiple positive periodic solutions of (1.3) Our aim of this article is to study ... main results of this article are following sufficient conditions which guarantee the existence of a periodic solution for (1.1) Theorem 1.1 Assume that there exist constants m < M, r > such that ... M ], then (1.1) has at least one ω-periodic solution x with m ≤ x ≤ M Some examples In this section, we present three examples to illustrate our conclusions Example 2.1 Consider the difference...
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