Solving initial-boundary value problems for coupled systems of partial differential equations
Solving Large Nonlinear Systems of Equations by an Adaptive Condensation Process.
Solving large-scale quadratic eigenvalue problems with Hamiltonian eigenstructure using a structure-preserving Krylov subspace method.
Solving Linear Ordinary Differential Equations by Exponentials of Iterated Commutators.
Solving linear systems with a Levinson-like solver.
Solving nonlinear boundary value problems using He's polynomials and Padé approximants.
Solving of heat shock on a hybrid system
Solving ordinary differential equation systems by approximation in a graphical way.
Solving Ratio-Dependent Predator-Prey System with Constant Effort Harvesting using Variational Iteration Method
Due to wide range of interest in use of bio-economic models to gain insight into the scientific management of renewable resources like fisheries and forestry,variational iteration method (VIM) is employed to approximate the solution of the ratio-dependent predator-prey system with constant effort prey harvesting.The results are compared with the results obtained by Adomian decomposition method and reveal that VIM is very effective and convenient for solving nonlinear differential equations.
Solving singular convolution equations using the inverse fast Fourier transform
The inverse Fast Fourier Transform is a common procedure to solve a convolution equation provided the transfer function has no zeros on the unit circle. In our paper we generalize this method to the case of a singular convolution equation and prove that if the transfer function is a trigonometric polynomial with simple zeros on the unit circle, then this method can be extended.
Solving Systems of Polynomial Equations by Bounded and Real Homotopy.
Solving systems of two–sided (max, min)–linear equations
A finite iteration method for solving systems of (max, min)-linear equations is presented. The systems have variables on both sides of the equations. The algorithm has polynomial complexity and may be extended to wider classes of equations with a similar structure.
Solving the Abel integral equation by interpolation methods
Solving the axisymmetric inverse heat conduction problem by a wavelet dual least squares method.
Solving the Cahn-Hilliard variational inequality with a semi-smooth Newton method
The Cahn-Hilliard variational inequality is a non-standard parabolic variational inequality of fourth order for which straightforward numerical approaches cannot be applied. We propose a primal-dual active set method which can be interpreted as a semi-smooth Newton method as solution technique for the discretized Cahn-Hilliard variational inequality. A (semi-)implicit Euler discretization is used in time and a piecewise linear finite element discretization of splitting type is used in space leading...
Solving the Cahn-Hilliard variational inequality with a semi-smooth Newton method
The Cahn-Hilliard variational inequality is a non-standard parabolic variational inequality of fourth order for which straightforward numerical approaches cannot be applied. We propose a primal-dual active set method which can be interpreted as a semi-smooth Newton method as solution technique for the discretized Cahn-Hilliard variational inequality. A (semi-)implicit Euler discretization is used in time and a piecewise linear finite element discretization of splitting type is used in space...
Solving the multidimensional difference biharmonic equation by the Monte Carlo method.
Solving the quintic by iteration in three dimensions.
Solving the Second Boundary value Problem in four space Variables
Solving the systems of equations arising in the discretization of some nonlinear p.d.e.'s by implicit Runge-Kutta methods