A modified quasi-boundary value method for a class of abstract parabolic ill-posed problems.
A modified regularization method.
A modified van der Pol equation with delay in a description of the heart action
In this paper, a modified van der Pol equation is considered as a description of the heart action. This model has a number of interesting properties allowing reconstruction of phenomena observed in physiological experiments as well as in Holter electrocardiographic recordings. Our aim is to study periodic solutions of the modified van der Pol equation and take into consideration the influence of feedback and delay which occur in the normal heart action mode as well as in pathological modes. Usage...
A modified version of explicit Runge-Kutta methods for energy-preserving
In this paper, Runge-Kutta methods are discussed for numerical solutions of conservative systems. For the energy of conservative systems being as close to the initial energy as possible, a modified version of explicit Runge-Kutta methods is presented. The order of the modified Runge-Kutta method is the same as the standard Runge-Kutta method, but it is superior in energy-preserving to the standard one. Comparing the modified Runge-Kutta method with the standard Runge-Kutta method, numerical experiments...
A monotone iterative method for boundary value problems of parametric differential equations.
A monotone method for constructing extremal solutions to second order periodic boundary value problems
We describe a constructive method which yields two monotone sequences that converge uniformly to extremal solutions to the periodic boundary value problem u''(t) = f(t,u(t),u'(t)), u(0) = u(2π), u'(0) = u'(2π) in the presence of a lower solution α(t) and an upper solution β(t) with β(t) ≤ α(t).
A multidimensional singular boundary value problem of Cauchy-Nicoletti type.
A multiplicity fixed point theorem in Fréchet spaces.
A multiplicity result for periodic solutions to higher-order ordinary differential equations via the method of upper and lower solutions.
A Nearly-Periodic Boundary Value Problem for Second Order Differential Equations
A necessary and sufficient condition for normality of linear control system with delays
A necessary and sufficient condition for stability of the convex combination of polynomials
A necessary and sufficient condition for the existence of positive solutions to singular boundary-value problems of higher order differential equations.
A necessary and sufficient condition for the oscillation in a class of even order neutral differential equations.
A necessary and sufficient condition for uniqueness of solutions of singular differential inequalities.
A necessary condition for twin boundary layer behavior
A Neumann boundary-value problem on an unbounded interval.
A new a priori estimate for multi-point boundary-value problem.
A new algorithm for the SVD of a long product of matrices and the stability of products.
A new application of the homotopy analysis method in solving the fractional Volterra's population system
This paper considers a Volterra's population system of fractional order and describes a bi-parametric homotopy analysis method for solving this system. The homotopy method offers a possibility to increase the convergence region of the series solution. Two examples are presented to illustrate the convergence and accuracy of the method to the solution. Further, we define the averaged residual error to show that the obtained results have reasonable accuracy.