The non-polynomial spline method is proposed to solve a non-linear system of the second-order boundary value problems (BVPs). Some numerical results are given to demostrate the validity and applicability of the presented ...

In this paper, we find numerical solution of x(t) + lambda integral(b)(a)k(t,s)x(s)ds = y(t) a <= t <= b or x(t) + lambda integral(b)(a) k(t,s)x(s)ds = y(t) a <= t <= b, a <= s <= b by Local Polynomial ...

In the present report we examine the dynamics exhibited by the solution of Bratu's equation. It represents a one-dimensional map with control parameter theta. For certain values of the parameter theta it exhibits successive ...

In this paper, we discussed a fifth-degree B-spline solution for the numerical solution to nonlinear fourth-order boundary value problems (BVPs) with separated boundary conditions. Two numerical examples are given to ...

We use B-spline functions to develop a numerical method for computing approximations to the solution of non-linear singular boundary value problems associated with physiology science. The original differential equation is ...

Chaos theory is considered a novel way of understanding the behaviour of nonlinear dynamic systems. It is well known that the evaluation of chaotic systems is dependent on initial conditions since exponential growth error ...

In this paper, the boundary value problem for the one-dimensional heat equation with a nonlocal initial condition is examined by using the third degree B-splines functions. The numerical solution of the equations are ...

In this paper, we extended the LPR method to solve the partial differential equations. Numerical experiments are presented to demonstrate the utility and the efficiency of the proposed computational procedure.