Computing accurate solution for coupled systems of second order partial differential equations. II. (English) Zbl 0813.65114
Summary: [For part I see ibid. 37, No. 3-4, 201-212 (1990; Zbl 0736.35052).]
An infinite series solution for solving nonhomogeneous coupled systems of second order partial differential equations is proposed. Given a finite domain and an admissible error \(\varepsilon\) we construct an analytical approximate solution whose error is uniformly bounded by \(\varepsilon\) in the given domain.
An infinite series solution for solving nonhomogeneous coupled systems of second order partial differential equations is proposed. Given a finite domain and an admissible error \(\varepsilon\) we construct an analytical approximate solution whose error is uniformly bounded by \(\varepsilon\) in the given domain.
MSC:
| 65M70 | Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs |
| 65M15 | Error bounds for initial value and initial-boundary value problems involving PDEs |
| 35K15 | Initial value problems for second-order parabolic equations |
| 35K45 | Initial value problems for second-order parabolic systems |
| 35C10 | Series solutions to PDEs |
Keywords:
error bound; coupled partial differential system; initial-boundary value problem; truncation; upper error bound; accuracy; analytical approximate solutionCitations:
Zbl 0736.35052References:
| [1] | Apostol T. M., Mathematical Analysis · Zbl 0309.26002 |
| [2] | Boyce W. E., Elementary Differential Equations and Boundary Value Problems (1977) · Zbl 0353.34001 |
| [3] | DOI: 10.1137/0124061 · Zbl 0236.35026 · doi:10.1137/0124061 |
| [4] | Courant R., Methods of Mathematical Physics (1962) · Zbl 0099.29504 |
| [5] | Chiu H. H., Quarterly Appl Maths. pp 87– (1969) |
| [6] | Dunford N., Linear Operators I (1957) · Zbl 0056.34601 |
| [7] | Hill J. M., Analytical aspects of heat flow in random two-component laminates pp 353– (1988) |
| [8] | DOI: 10.1080/00207169008803948 · Zbl 0736.35052 · doi:10.1080/00207169008803948 |
| [9] | DOI: 10.1016/0022-247X(82)90116-0 · Zbl 0493.35051 · doi:10.1016/0022-247X(82)90116-0 |
| [10] | DOI: 10.1137/1020098 · Zbl 0395.65012 · doi:10.1137/1020098 |
| [11] | Ortega J. M., Iterative Solution of Nonlinear Equations in Several Variables (1970) · Zbl 0241.65046 |
| [12] | DOI: 10.1002/fld.1650070703 · Zbl 0639.76112 · doi:10.1002/fld.1650070703 |
| [13] | Zachmanoglou E. C., Introduction to Partial Differential Equations with Applications (1976) · Zbl 0327.35001 |
| [14] | Zygmund A., Trigonometric Series (1977) |
| [15] | Gradshteyn I. S., Tables of Integrals, Series, and Products (1980) · Zbl 0521.33001 |
| [16] | Churchill R. V., Fourier Series and Boundary Value Problems (1978) · Zbl 0378.42001 |
| [17] | Lancaster P., The Theory of Matrices (1985) · Zbl 0578.62099 |
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