Exact and analytic numerical solution of coupled parabolic mixed problems in a semi-infinite medium
This paper deals with mixed problems of the type \[ u_t= Au+ Cu_{xx},\quad x<0,\;t>0, \qquad u(x,0)= g(x), \quad x\geq 0, \qquad u(0,t)= f(t), \quad t\geq 0, \] where \(u(x,t)\), \(g(x)\), and \(f(t)\) are \(m\)-dimensional vectors in \(\mathbb{C}^m\) and \(A\), \(C\) are matrices in \(\mathbb{C}^{m\times m}\). Using sine Fourier transforms, an exact expression of the exact solution is given.
scientific article; zbMATH DE number 2075467
scientific article