The Goursat problem, which is related to hyperbolic partial differential equations, occurs in a variety of branches physics and engineering. We studied the solution equation utilizing reduced transform (RDT) Adomian decomposition (AD) techniques this inquiry. problem's analytical found series form, converges exact solutions. approaches' reliability efficiency were evaluated using problems (line...

In present article the self-contained derivation of eigenvalue inverse problem results is given by using a discrete approximation of the Schrödinger operator on a bounded interval as a finite three-diagonal symmetric Jacobi matrix. This derivation is more correct in comparison with previous works which used only single-diagonal matrix. It is demonstrated that inverse problem procedure is nothin...

The problem of constructing semi-discrete integrable analogues the Liouville type PDE is discussed. We call equation a discretization if these two equations have common integral. For from well-known Goursat list for which integrals minimal order are less than or equal to we presented corresponding versions. contains new examples non-autonomous Darboux chains.

We find the exact analytical solution to a Goursat PDE system governing the kernels of a backsteppingbased boundary control law that stabilizes a constant-coefficient 2 × 2 system of first-order hyperbolic linear PDEs. The solution to the Goursat system is related to the solution of a simpler, explicitly solvable Goursat system through a suitable infinite series of powers of partial derivatives...