In this article, a fourth order quintic spline method has been developed to obtain numerical solutions for second order
boundary value problems with Dirichlet boundary conditions. The developments of the quintic spline method and
convergence analysis were presented. Three test problems have been considered for comparison purposes. The numerical
results showed that the quintic spline method is more accurate compared to existing cubic spline method when solving
nonlinear second order boundary value problems but vice versa when solving linear second order boundary value
problems.
In this paper we prove the existence of ϒ-fixed point for a multidimensional nonlinear mappings F : Xk → X defined on the partially ordered metric spaces and satisfying (ψ, θ, ϕ)-weak contractive conditions. Moreover, we prove the uniqueness of that fixed point under extra conditions to (ψ, θ, ϕ)-weak contractive conditions.