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Page 467 of Mathematical Reviews Vol. , Issue 94a [page]

1994 Mathematical Reviews  
In the proof one estimates the uniform bound for the approximate solutions and the H,. compactness for the entropy dissipation measures associated with all weak entropy pairs.  ...  The proof of the existence of a solution of the latter is based on reducing it to a system of integro-differential equations and applying the Bubnov-Galerkin process to prove the existence and uniqueness  ... 

Page 1172 of Mathematical Reviews Vol. , Issue 97B [page]

1997 Mathematical Reviews  
Summary: “A numerical method is proposed to approximate the solution of a nonlinear and nonlocal system of integro-differential equations describing age-dependent population dynamics with spa- tial diffusion  ...  The existence and uniqueness of the approximate solutions are proved and error estimates are obtained using a standard argument (dis- crete energy estimates) for the numerical solution of linear para-  ... 

Page 7314 of Mathematical Reviews Vol. , Issue 2000j [page]

2000 Mathematical Reviews  
Bruno Scheurer (Bruyéres-le-Chatel) 2000j:65093 65M60 45K05 Jiang, Ziwen (PRC-SHDN; Jinan) L™(L*) and L®°(L°) error estimates for mixed methods for integro-differential equations of parabolic type.  ...  , for a mixed finite element method for the initial-boundary value problem for the integro-differential equation u, = div{aVu+ Ps b\Vudt+ ¢ cudt}+ f based on the Raviart-Thomas space V, x Wi, C H(div;Q  ... 

Page 3112 of Mathematical Reviews Vol. , Issue 2000e [page]

2000 Mathematical Reviews  
criteria for solutions of impulsive integro-differential equations in Banach spaces (87- 102); Chunging Lu, On the existence of multiple solutions of two-dimensional steady flow in a porous channel (103  ...  Mooney, Iterative solution of implicit approximations for parabolic and hyperbolic quenching problems (133-144). V. W.  ... 

Page 1644 of Mathematical Reviews Vol. , Issue 83d [page]

1983 Mathematical Reviews  
The authors are concerned with the numerical approximation of a class of linear neutral functional-differential equations.  ...  The Trotter-Kato theorem is applied to prove the convergence of numerical schemes involving splines for a sequence of approximating higher order ordinary differential equations.  ... 

Page 607 of Mathematical Reviews Vol. , Issue 86b [page]

1986 Mathematical Reviews  
Shock formation in smooth solutions of the scalar integro-differential conservation law from part I is demonstrated through detailed numerical experiments—this completes the basic argument from part I.  ...  of approximate solutions to a weak solution also holds for this class of approximations.  ... 

Page 1247 of Mathematical Reviews Vol. , Issue 2001B [page]

2001 Mathematical Reviews  
The authors study finite volume element approximations for a class of integro-differential equations in two space dimensions. The numerical method is a linear finite volume element method.  ...  A thorough analysis of three problems involving differ- ence schemes for partial differential equations of hyperbolic type is provided. {For the entire collection see MR 2000j:65009. } Thomas H.  ... 

Page 455 of Mathematical Reviews Vol. , Issue 96a [page]

1996 Mathematical Reviews  
solutions of hyperbolic problems.  ...  He derives local discrete entropy inequalities for the schemes built on Godunov’s numerical flux as a lemma, and proves convergence of u; to the entropy solution u of the conservation laws in Lf, 1 < p  ... 

Page 3250 of Mathematical Reviews Vol. , Issue 87f [page]

1987 Mathematical Reviews  
Summary: “Numerically, moving grids are often found to improve the resolution of approximate solutions to nonlinear hyperbolic conservation laws.  ...  Phys. 52 (1983), no. 2, 374-389] and generalizes the results of the author on the particle approximation of hyperbolic equations {the author, Numerical methods in fluid dynamics (Como, 1983), 243-324,  ... 

Page 3320 of Mathematical Reviews Vol. , Issue 2001E [page]

2001 Mathematical Reviews  
This second-order accurate scheme is applied to the integro-differential equations of the BGK approximation to Boltzmann’s equation. Thomas P.  ...  Summary: “Here the strategy of the group explicit method is ap- plied to the numerical solution of a linear dispersive equation.  ... 

Page 5147 of Mathematical Reviews Vol. , Issue 96i [page]

1996 Mathematical Reviews  
Baker, Dynamics of discretized equations for DDE’s (145- 151); Athena Makroglou, Regions of stability for extended back- ward differentiation methods in the numerical solution of Volterra integro-differential  ...  Baker and Arsalang Tang, Numerical solution of Volterra integro- differential equations with an unbounded delay (129-136); W. H.  ... 

Page 3350 of Mathematical Reviews Vol. , Issue 92f [page]

1992 Mathematical Reviews  
Shen (Minneapolis, MN) 65 NUMERICAL ANALYSIS 92f:65066 65310 45305 65F10 65R20 Fodchuk, O. V. A variational-iterative method for solving boundary value problems for integro-differential equations.  ...  Summary: “The defects which are caused by the solutions of approximations to an original equation provide an effective tool for asymptotically exact estimation of approximation errors.  ... 

Page 1527 of Mathematical Reviews Vol. , Issue 96c [page]

1996 Mathematical Reviews  
Here the author shows a converse of this result, namely, that the approximation Umog built from the unique entropy solutions of the coupled modulation equations approximates periodic weak solu- tions of  ...  Differential Equations 113 (1994), no. 2, 473-504. In the paper under review, the author considers approximate solutions to spatially one-dimensional systems of conservation laws.  ... 

Author index to volume 72 (1996)

1996 Journal of Computational and Applied Mathematics  
Simos, A generator of high-order embedded P-stable methods for the numerical solution of the Schr6dinger equation Babovsky, H., Recognition of ring pairs in the data analysis of Cherenkov detectors Bainov  ...  Minchev, Forced oscillation of solutions of certain hyperbolic equations of neutral type Baotong, C., see Bainov, D. Brunon, E., see Hureau, J. Caehafeiro, A. and C.  ...  Nieto, Boundary value problems for second order integro-differential equations of Fredholm type Luzyanina, T. and D.  ... 
doi:10.1016/s0377-0427(96)90057-6 fatcat:yndvvlqaqbez5assa2nbsmgcoe

Page 3746 of Mathematical Reviews Vol. , Issue 2003e [page]

2003 Mathematical Reviews  
Summary: “In this article, the effect of numerical quadrature on the finite element Galerkin approximations to the solution of hy- perbolic equations is studied.  ...  , Graeme (1-CSM-CS; Golden, CO) H'-Galerkin mixed finite element methods for parabolic partial integro-differential equations.  ... 
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