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A matrix constructive method for the analytic-numerical solution of coupled partial differential systems
Applications of Mathematics, Tome 40 (1995) no. 5, pp. 391-400
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In this paper we construct analytic-numerical solutions for initial-boundary value systems related to the equation $u_t-Au_{xx}-Bu=0$, where $B$ is an arbitrary square complex matrix and $A$ ia s matrix such that the real part of the eigenvalues of the matrix $\frac{1}{2}(A+A^H)$ is positive. Given an admissible error $\varepsilon $ and a finite domain $G$, and analytic-numerical solution whose error is uniformly upper bounded by $\varepsilon $ in $G$, is constructed.
In this paper we construct analytic-numerical solutions for initial-boundary value systems related to the equation $u_t-Au_{xx}-Bu=0$, where $B$ is an arbitrary square complex matrix and $A$ ia s matrix such that the real part of the eigenvalues of the matrix $\frac{1}{2}(A+A^H)$ is positive. Given an admissible error $\varepsilon $ and a finite domain $G$, and analytic-numerical solution whose error is uniformly upper bounded by $\varepsilon $ in $G$, is constructed.
DOI : 10.21136/AM.1995.134302
Classification : 15A24, 15A45, 15A60, 35K15, 65F15, 65M70, 65N15
Keywords: Schur decomposition; partial differential system; eigenvalues bound; matrix norms; analytic-numerical solution; error bounds 
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Jódar, Lucas; Navarro, Enrique; Ferrer, M. V. A matrix constructive method for the analytic-numerical solution of coupled partial differential systems. Applications of Mathematics, Tome 40 (1995) no. 5, pp. 391-400. doi: 10.21136/AM.1995.134302

[1] T.M. Apostol: Mathematical Analysis. Addison-Wesley, Reading M.A., 1977.

[2] F.L. Bauer, A.S. Householder: Absolute norms and characteristic roots. Numerische Math. 3 (1961), 241–246. | DOI | MR

[3] I.E. Butsenieks, E.V. Shcherbinin: Magnetohydrodynamic flow in electrodynamically coupled rectangular ducts I. Magn. Girodinam 2 (1976), 35–40.

[4] J.R. Cannon, R.E. Klein: On the observability and stability of the temperature distribution in a composite head conductor. SIAM J. Appl. Math. 24 (1973), 596–602. | DOI | MR

[5] H.H. Chiu: Theory of irreducible linear systems. Quart. Appl. Maths. XXVII (1969), 87–104. | DOI | MR

[6] R.V. Churchill, J.W. Brown: Fourier Series and Boundary Value Problems. McGraw-Hill, New York, 1978. | MR

[7] R. Courant, D. Hilbert: Methods of Mathematical Physics, Vol. II. Interscience, New York, 1962. | MR

[8] G.H. Golub, C.F. van Loan: Matrix Computations. Johns Hopkins Univ. Press, Baltimore M.A., 1985.

[9] K. Gopalsamy: An arms race with deteriorating armaments. Math. Biosci. 37 (1977), 191–203. | DOI | MR | Zbl

[10] J.M. Hill, J.R. Willis: Analytic aspects of heat flow in random two-component laminates. Quart. Appl. Maths. 46 (1988), no. 2, 353–364. | DOI | MR

[11] L. Jódar: Computing accurate solutions for coupled systems of second order partial differential equations. Int. J. Computer Math. 37 (1990), 201–212. | DOI

[12] L. Jódar: Computing accurate solutions for coupled systems of second order partial differential equations II. Int. J. Computer Math. 46 (1992), 63–75. | DOI

[13] A.I. Lee, J.M. Hill: On the general linear coupled system for diffusion in media with two diffusivities. J. Math. Anal. Appl. 89 (1982), 530–557. | DOI | MR

[14] M. Mascagni: An initial-boundary value problem of physiological significance for equations of nerve conduction. Com. Pure Appl. Math. XLII (1989), 213–227. | DOI | MR | Zbl

[15] M. Mascagni: The backward Euler method for numerical solution of the Hodgkin-Huxley equations of nerve condition. SIAM J. Numer. Anal. 27 (1990), no. 4, 941–962. | DOI | MR

[16] M. Mascagni: A parallelizing algorithm for compution solutions to arbitrarily branched cable neutron models. J. Neurosc. Methods 36 (1991), 105–114. | DOI

[17] C.B. Moler, C.F. van Loan: Nineteen dubious ways to compute the exponential of a matrix. SIAM Review 20 (1978), 801–836. | DOI | MR

[18] M. Sezgin: Magnetohydrodynamic flow in an infinite channel. Int. J. Numer. Methods Fluids 6 (1986), 593–609. | DOI | Zbl

[19] J. Stoer, R. Bulirsch: Introduction to Numerical Analysis. Springer-Verlag, New York, 1980. | MR

[20] K.S. Yee: Explicit solutions for the initial boundary value problem of a system of lossless transmission lines. SIAM J. Appl. Math. 24 (1975), 62–80. | DOI | MR

[21] E.C. Zachmanoglou, D.W. Thoe: Introduction to Partial Differential Equations with Applications. William and Wilkins, Baltimore, 1976. | MR

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