Smooth Solutions of Initial-Value Problems in Regions with Corners

Solutions of initial and boundary value problems via F-contraction mappings in metric-like space

We present sufficient conditions for the existence of solutions of second-order two-point boundary value and fractional order functional differential equation problems in a space where self distance is not necessarily zero. For this, first we introduce a Ciric type generalized F-contraction and F- Suzuki contraction in a metric-like space and give relevance to fixed point results. To illustrate...

Computing Exact Solutions of Initial Value Problems

Finding the exact solution of initial value problems is the main topic of this thesis. Because differential equations in practice can be hard to solve, we require algorithms to solve them on a computer. Since the solution of the equation needs to be stored on a computer, we first discuss the representation of real functions. We show that approximating a function by polynomials gives a suitable ...

Approximating Initial-Value Problems with Two-Point Boundary-Value Problems: BBM-Equation

Nonlinear Initial Value Problems with Positive Global Solutions

We give conditions on m(t), p(t), and f(t, y, z) so that the nonlinear initial value problem (1/m(t)(p(t)y0)0 + f(t, y, p(t)y0) = 0, for t > 0, y(0) = 0, limt→0+ p(t)y0(t) = B > 0, has at least one positive solution which exists for all t > 0, if B is sufficiently small. We allow a singularity at t = 0 so the solution y0(t) may be unbounded near t = 0.

Piecewise-linearized methods for initial-value problems with oscillating solutions

Two piecewise-linearized methods for the numerical solution of nonlinear second-order differential equations which contain the first-order derivative are presented. These methods provide piecewise analytical solutions in open intervals, result in explicit finite difference equations for both the displacement and the velocity or only the displacement, at nodal points, and continuous solutions ev...