Fifth-order numerical methods for heat equation subject to a boundary integral specification.
Fifth-order Runge-Kutta with higher order derivative approximations.
Filippov approach in stochastic maximum principle without differentiability assumptions.
Filippov Lemma for certain second order differential inclusions
In the paper we give an analogue of the Filippov Lemma for the second order differential inclusions with the initial conditions y(0) = 0, y′(0) = 0, where the matrix A ∈ ℝd×d and multifunction is Lipschitz continuous in y with a t-independent constant l. The main result is the following: Assume that F is measurable in t and integrably bounded. Let y 0 ∈ W 2,1 be an arbitrary function fulfilling the above initial conditions and such that where p 0 ∈ L 1[0, 1]. Then there exists a solution y ∈ W 2,1...
Filippov Lemma for matrix fourth order differential inclusions
In the paper we give an analogue of the Filippov Lemma for the fourth order differential inclusions y = y”” - (A² + B²)y” + A²B²y ∈ F(t,y), (*) with the initial conditions y(0) = y’(0) = y”(0) = y”’(0) = 0, (**) where the matrices are commutative and the multifunction is Lipschitz continuous in y with a t-independent constant l < ||A||²||B||². Main theorem. Assume that y₀ ∈ W4,1
Filippov's operation and some attributes
Filippov's theorem for impulsive differential inclusions with fractional order.
Finding Liouvillian first integrals of rational ODEs of any order in finite terms.
Finding of the general integral of differential equations by means of Taylor series and finding of some form of non-Cauchy's particular integrals
Finding the Boundary Curves of the Third Order Linear Ordinary Differential Equation
Fine scales of decay of operator semigroups
Motivated by potential applications to partial differential equations, we develop a theory of fine scales of decay rates for operator semigroups. The theory contains, unifies, and extends several notable results in the literature on decay of operator semigroups and yields a number of new ones. Its core is a new operator-theoretical method of deriving rates of decay combining ingredients from functional calculus and complex, real and harmonic analysis. It also leads to several results of independent...
Finite and infinite order of growth of solutions to linear differential equations near a singular point
In this paper, we investigate the growth of solutions of a certain class of linear differential equation where the coefficients are analytic functions in the closed complex plane except at a finite singular point. For that, we will use the value distribution theory of meromorphic functions developed by Rolf Nevanlinna with adapted definitions.
Finite Difference Methods and Their Convergence for a Class of Singular Two Point Boundary Value Problems.
Finite difference methods for computing eigenvalues of fourth order boundary value problems.
Finite eigenfunction approximations for continuous spectrum operators.
Finite element methods for elliptic mixed boundary value problems containing singularities
Finite element methods for linear coupled thermoelasticity
Finite element solution of nonlinear elliptic equations with discontinuous coefficients and approximations in Sobolev-Slobodeckij spaces
Finite elements and numerical stability
Finite order solutions of complex linear differential equations.