A first order accuracy scheme on non-uniform mesh.
A fixed point method to compute solvents of matrix polynomials
Matrix polynomials play an important role in the theory of matrix differential equations. We develop a fixed point method to compute solutions of matrix polynomials equations, where the matricial elements of the matrix polynomial are considered separately as complex polynomials. Numerical examples illustrate the method presented.
A full multigrid method for semilinear elliptic equation
A full multigrid finite element method is proposed for semilinear elliptic equations. The main idea is to transform the solution of the semilinear problem into a series of solutions of the corresponding linear boundary value problems on the sequence of finite element spaces and semilinear problems on a very low dimensional space. The linearized boundary value problems are solved by some multigrid iterations. Besides the multigrid iteration, all other efficient numerical methods can also serve as...
A Galerkin method of for singular boundary value problems.
A Galerkin Method with Modified Piecewise Polynomials for Solving a Second-Order Boundary Value Problem.
A high accuracy method for solving ODEs with continuous right-hand side.
A High Order Projection Method for Nonlinear Two Point Boundary Value Problems.
A higher order approximation to a singular perturbation problem.
A higher-order method for nonlinear singular two-point boundary value problems.
A Hopf Bifurcation Theorem for Difference Equations Approximating a Differential Equation.
A Jacobi dual-Petrov-Galerkin method for solving some odd-order ordinary differential equations.
A Laplace decomposition algorithm applied to a class of nonlinear differential equations.
A method for determining constants in the linear combination of exponentials
Shifting a numerically given function we obtain a fundamental matrix of the linear differential system with a constant matrix . Using the fundamental matrix we calculate , calculating the eigenvalues of we obtain and using the least square method we determine .
A method for finding the step size of integration of a system of ordinary differential equations
A method of discretization for the Lagerström-Cole model equation.
A mixed finite element method for Darcy flow in fractured porous media with non-matching grids
We consider an incompressible flow problem in a N-dimensional fractured porous domain (Darcy’s problem). The fracture is represented by a (N − 1)-dimensional interface, exchanging fluid with the surrounding media. In this paper we consider the lowest-order (ℝ T0, ℙ0) Raviart-Thomas mixed finite element method for the approximation of the coupled Darcy’s flows in the porous media and within the fracture, with independent meshes for the respective domains. This is achieved thanks to an enrichment...
A mixed finite element method for Darcy flow in fractured porous media with non-matching grids∗
We consider an incompressible flow problem in a N-dimensional fractured porous domain (Darcy’s problem). The fracture is represented by a (N − 1)-dimensional interface, exchanging fluid with the surrounding media. In this paper we consider the lowest-order (ℝ T0, ℙ0) Raviart-Thomas mixed finite element method for the approximation of the coupled Darcy’s flows in the porous media and within the fracture, with independent meshes for the respective...
A model of macroscale deformation and microvibration in skeletal muscle tissue
This paper deals with modeling the passive behavior of skeletal muscle tissue including certain microvibrations at the cell level. Our approach combines a continuum mechanics model with large deformation and incompressibility at the macroscale with chains of coupled nonlinear oscillators. The model verifies that an externally applied vibration at the appropriate frequency is able to synchronize microvibrations in skeletal muscle cells. From the numerical analysis point of view, one faces...
A Modified Continuation Method for the Numerical Solution of Nonlinear Two-Point Boundary Value Problems by Shooting Techniques.
A Modified Newton Method for the Solution of Ill-Conditioned Systems of Nonlinear Equations with Application to Multiple Shooting .