Abstract
In this paper, a method to construct an analytic-numerical solution for homogeneous parabolic coupled systems with homogeneous boundary conditions of the type ut = Auxx, A1u(o,t) + B1ux(o,t) = 0, A2u(1,t) + B2ux(1,t) = 0, ot>0, u (x,0) = f(x), where A is a positive stable matrix and A1, B1, B1, B2, are arbitrary matrices for which the block matrix is non-singular, is proposed.
Highlights
Coupled partial differential systems with coupled boundary-value conditions are frequent in different areas of science and technology, as in scattering problems in Quantum Mechanics [1]-[3], in Chemical Physics [4]-[6], coupled diffusion problems [7]-[9], modelling of coupled thermoelastoplastic response of clays subjected to
The solution of these problems has motivated the study of vector and matrix SturmLiouville problems, see [11]-[14] for example
(c) Other problem is the calculation of the matrix exponential, which may present difficulties, see [21] [22]. For this reason we propose in this paper to solve the following problem: Given an admissible error ε > 0 and a bounded subdomain D[t0=,t1 ] [0,1]×[t0,t1 ], t0 > 0
Summary
Coupled partial differential systems with coupled boundary-value conditions are frequent in different areas of science and technology, as in scattering problems in Quantum Mechanics [1]-[3], in Chemical Physics [4]-[6], coupled diffusion problems [7]-[9], modelling of coupled thermoelastoplastic response of clays subjected to. ( ) ( ) Ker B 1 − b1I Ker B 2 − b2I is an invariant subspace with respect to matrix A, where a subspace E of m is invariant by the matrix A ∈ m×m if A( E ) ⊂ E , we can construct an exact series solution u ( x,t ) of homogeneous problem (1)-(4). ( ) ( ) Ker B 1 ∩ Ker A 2 − a2I is an invariant subspace respect to matrix A, we can construct an exact series solution u ( x,t ) of homogeneous problem (1)-(4).
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