Numerical Solution of a Hyperbolic Free Boundary Problem with a Method of Characteristics.
Numerical solution of an inverse initial boundary value problem for the wave equation in the presence of conductivity imperfections of small volume
We consider the numerical solution, in two- and three-dimensional bounded domains, of the inverse problem for identifying the location of small-volume, conductivity imperfections in a medium with homogeneous background. A dynamic approach, based on the wave equation, permits us to treat the important case of “limited-view” data. Our numerical algorithm is based on the coupling of a finite element solution of the wave equation, an exact controllability method and finally a Fourier inversion for localizing...
Numerical solution of an inverse initial boundary value problem for the wave equation in the presence of conductivity imperfections of small volume
We consider the numerical solution, in two- and three-dimensional bounded domains, of the inverse problem for identifying the location of small-volume, conductivity imperfections in a medium with homogeneous background. A dynamic approach, based on the wave equation, permits us to treat the important case of “limited-view” data. Our numerical algorithm is based on the coupling of a finite element solution of the wave equation, an exact controllability method and finally a Fourier inversion for...
Numerical Solution of Steady-State Porous Flow Free Boundary Problems.
Numerical solutions of a fractional predator-prey system.
Numerical solutions to integral equations equivalent to differential equations with fractional time
This paper presents an approximate method of solving the fractional (in the time variable) equation which describes the processes lying between heat and wave behavior. The approximation consists in the application of a finite subspace of an infinite basis in the time variable (Galerkin method) and discretization in space variables. In the final step, a large-scale system of linear equations with a non-symmetric matrix is solved with the use of the iterative GMRES method.
Numerical solutions to the Darboux problem with functional dependence.
Numerical study of free interface problems using boundary integral methods.