Second derivative linear multistep formula and its stability on the imaginary axis
Second Order Nonlinear Differential Equations Equivalent To Linear Differential Equations
Second order nonlinear differential equations equivalent to linear differential equations.
Simulation of analog computer in solving non-linear differential equations by a digital computer
Singular solutions of a singular differential equation.
Smooth factorizations of matrix valued functions and their derivatives.
Solution of an extraordinary differential equation by Adomian decomposition method.
Solutions of nonhomogeneous linear differential equations with exceptionally few zeros.
Solutions to Lyapunov stability problems: Nonlinear systems with continuous motions.
Solutions to Lyapunov stability problems of sets: Nonlinear systems with differentiable motions.
Solvability of an Infinite System of Singular Integral Equations
2000 Mathematics Subject Classification: 45G15, 26A33, 32A55, 46E15.Schauder's fixed point theorem is used to establish an existence result for an infinite system of singular integral equations in the form: (1) xi(t) = ai(t)+ ∫t0 (t − s)− α (s, x1(s), x2(s), …) ds, where i = 1,2,…, α ∈ (0,1) and t ∈ I = [0,T]. The result obtained is applied to show the solvability of an infinite system of differential equation of fractional orders.
Solvability of nonlinear Langevin equation involving two fractional orders with Dirichlet boundary conditions.
Solving dynamical systems with cubic trigonometric splines.
Solving nonlinear boundary value problems using He's polynomials and Padé approximants.
Some compactness methods in the theory of nonlinear evolution equations with applications to P.D.E.
Some fixed point theorems in locally convex spaces and applications to differential and integral equations
Some remarks on Nagumo's theorem
We provide a simpler proof for a recent generalization of Nagumo’s uniqueness theorem by A. Constantin: On Nagumo’s theorem. Proc. Japan Acad., Ser. A 86 (2010), 41–44, for the differential equation , and we show that not only is the solution unique but the Picard successive approximations converge to the unique solution. The proof is based on an approach that was developed in Z. S. Athanassov: Uniqueness and convergence of successive approximations for ordinary differential equations. Math....
Some remarks on the intervals of stability of Runge-Kutta methods after Richardson extrapolation
Special solutions of the Riccati equation with applications to the Gross-Pitaevskii nonlinear PDE.
Stability and B-Convergence of Linearly Implicit Runge-Kutta Methods.