Solvable two-body Dirac equation as a potential model of light mesons.
Solving a bilocal linear singularly perturbed problem.
Solving a class of generalized Lyapunov operator differential equations without the exponential operator function.
In this paper a method for solving operator differential equations of the type X' = A + BX + XD; X(0) = C0, avoiding the operator exponential function, is given. Results are applied to solve initial value problems related to Riccati type operator differential equations whose associated algebraic equation is solvable.
Solving a collection of free coexistence-like problems in stability
Solving a system of second order obstacle problems by a modified decomposition method.
Solving an inverse Sturm-Liouville problem by a Lie-group method.
Solving Differential Equations by Parallel Laplace Method with Assured Accuracy
The paper has been presented at the 12th International Conference on Applications of Computer Algebra, Varna, Bulgaria, June, 2006We produce a parallel algorithm realizing the Laplace transform method for the symbolic solving of differential equations. In this paper we consider systems of ordinary linear differential equations with constant coefficients, nonzero initial conditions and right-hand parts reduced to sums of exponents with polynomial coefficients.
Solving dynamical systems with cubic trigonometric splines.
Solving Equations, an Elegant Legacy
Solving higher order Fuchs type differential systems avoiding the increase of the problem dimension.
Solving linear differential equations by quadratures: Comments on a general procedure.
Solving Linear Ordinary Differential Equations by Exponentials of Iterated Commutators.
Solving nonlinear boundary value problems using He's polynomials and Padé approximants.
Solving of Volterra's linear integral equations
Solving ratio-dependent predator-prey system with constant effort harvesting using homotopy perturbation method.
Solving second-order singularly perturbed ODE by the collocation method based on energetic Robin boundary functions
For a second-order singularly perturbed ordinary differential equation (ODE) under the Robin type boundary conditions, we develop an energetic Robin boundary functions method (ERBFM) to find the solution, which automatically satisfies the Robin boundary conditions. For the non-singular ODE the Robin boundary functions consist of polynomials, while the normalized exponential trial functions are used for the singularly perturbed ODE. The ERBFM is also designed to preserve the energy, which can quickly...
Solving the Dirichlet acoustic scattering problem for a surface with added bumps using the Green's function for the original surface.
Solving two-point boundary value problems for the non monic regular matrix differential equation
Some addition to the generalized Riemann-Hilbert problem
We consider the generalized Riemann-Hilbert problem for linear differential equations with irregular singularities. If one weakens the conditions by allowing one of the Poincaré ranks to be non-minimal, the problem is known to have a solution. In this article we give a bound for the possibly non-minimal Poincaré rank. We also give a bound for the number of apparent singularities of a scalar equation with prescribed generalized monodromy data.
Some algebraic fixed point theorems for multi-valued mappings with applications
In this paper, some algebraic fixed point theorems for multi-valued discontinuous operators on ordered spaces are proved. These theorems improve the earlier fixed point theorems of Dhage (1988, 1991) Dhage and Regan (2002) and Heikkilä and Hu (1993) under weaker conditions. The main fixed point theorems are applied to the first order discontinuous differential inclusions for proving the existence of the solutions under certain monotonicity condition of multi-functions.