quartic non-polynomial spline function approximation in off step points is developed, for the solution of fourth-order boundary value problems. using consistency relation of such spline and suitable choice of parameter,we have obtained second, fourth and sixth orders methods. convergence analysis of sixth order method has been given. the methods are illustrated by some examples, to verify the or...

IT is intuitively obvious that if a simple continuous curve is given in the (x, 2/)-plane, and a continuous distribution of values along the curve, there will exist functions of x and y which are continuous in both variables together, and which take on the prescribed values along the curve. It is the purpose of the present note to give an analytic proof of this fact, by elementary means, and, i...

We consider the boundary value problem:    x (m) (t) = f (t, x(t)), a ≤ t ≤ b, m > 1 x(a) = β 0 ∆x (k) ≡ x (k) (b) − x (k) (a) = β k+1 , continuous at least in the interior of the domain of interest. We give a constructive proof of the existence and uniqueness of the solution, under certain conditions, by Picard's iteration. Moreover Newton's iteration method is considered for the numerical ...

In this paper, we give the spectral theory for eigenvalues and eigenfunctions of a boundary value problem consisting of the linear fractional Bessel operator. Moreover, we show that this operator is self-adjoint, the eigenvalues of the problem are real, and the corresponding eigenfunctions are orthogonal. In this paper, we give the spectral theory for eigenvalues and eigenfunctions...

this study concerns the existence and multiplicity of positive weak solutions for a class ofsemilinear elliptic systems with nonlinear boundary conditions. our results is depending onthe local minimization method on the nehari manifold and some variational techniques. alsoby using mountain pass lemma, we establish the existence of at least one solution withpositive energy.