Solution of a finite-dimensional problem with -mappings and diagonal multivalued operators.
Solution of a Nonlinear Two Point Boundary Value Problem .
Solution of a system of linear equations with given error sets for coefficients
In the paper, a method is given for finding all solutions of a system of linear equations with interval coefficients and with additional supposition that these coefficients fulfil a given system of homogeneous linear equations.
Solution of an extraordinary differential equation by Adomian decomposition method.
Solution of Cauchy-type singular integral equations of the first kind with zeros of Jacobi polynomials as interpolation nodes.
Solution of contaminant transport with adsorption in porous media by the method of characteristics
A new approximation scheme is presented for the mathematical model of convection-diffusion and adsorption. The method is based on the relaxation method and the method of characteristics. We prove the convergence of the method and present some numerical experiments in 1D. The results can be applied to the model of contaminant transport in porous media with multi-site, equilibrium and non-equilibrium type of adsorption.
Solution of contaminant transport with adsorption in porous media by the method of characteristics
A new approximation scheme is presented for the mathematical model of convection-diffusion and adsorption. The method is based on the relaxation method and the method of characteristics. We prove the convergence of the method and present some numerical experiments in 1D. The results can be applied to the model of contaminant transport in porous media with multi-site, equilibrium and non-equilibrium type of adsorption.
Solution of degenerate parabolic variational inequalities with convection
Degenerate parabolic variational inequalities with convection are solved by means of a combined relaxation method and method of characteristics. The mathematical problem is motivated by Richard’s equation, modelling the unsaturated – saturated flow in porous media. By means of the relaxation method we control the degeneracy. The dominance of the convection is controlled by the method of characteristics.
Solution of degenerate parabolic variational inequalities with convection
Degenerate parabolic variational inequalities with convection are solved by means of a combined relaxation method and method of characteristics. The mathematical problem is motivated by Richard's equation, modelling the unsaturated – saturated flow in porous media. By means of the relaxation method we control the degeneracy. The dominance of the convection is controlled by the method of characteristics.
Solution of doubly nonlinear and degenerate parabolic problems by relaxation schemes
Solution of Linear Equations with Hankel and Toeplitz Matrices.
Solution of mechanical problems in fractured rock with the user-defined interface of COMSOL multiphysics
This paper presents the main concept and several key features of the user-defined interface of COMSOL Java API for the solution of mechanical problems in fractured rock. This commercial computational system based on FEM has yet to incorporate fractures in mechanical problems. Our aim is to solve a 2D mechanical problem with a fracture which is defined separately from finite-element discretization and the fracture properties are included through the constitutive laws. This will be performed based...
Solution of Monotone Nonlinear Elliptic Boundary Value Problems.
Solution of multi-delay systems via combined block-pulse functions and Legendre polynomials.
Solution of nonlinear degenerate elliptic-parabolic systems in Orlicz-Sobolev spaces
Solution of non-linear equations systems by Newton's method and the gradients method
Solution of nonlinear Fredholm-Hammerstein integral equations by using semiorthogonal spline wavelets.
Solution of nonlinear Volterra-Hammerstein integral equations via single-term Walsh series method.
Solution of nonlinear Volterra-Hammerstein integral equations via rationalized Haar functions.
Solution of option pricing equations using orthogonal polynomial expansion
We study both analytic and numerical solutions of option pricing equations using systems of orthogonal polynomials. Using a Galerkin-based method, we solve the parabolic partial differential equation for the Black-Scholes model using Hermite polynomials and for the Heston model using Hermite and Laguerre polynomials. We compare the obtained solutions to existing semi-closed pricing formulas. Special attention is paid to the solution of the Heston model at the boundary with vanishing volatility.