Financial theory can incorporate fractional differential equation, which provides new concepts and methods for theoret- ical analysis practical implementations. In this research, a numerical method to solve time Black-Scholes European option pricing model is developed applied using extended cubic B-spline Caputo derivative. The graphical results shows that the prices from proposed technique agr...

This paper presents cubic spline interpolation based trajectory planning method which is aiming to achieve smooth biped robot walking trajectory. We first characterize the bipedal walking cycle and point out some major issues that need to be addressed to plan a continuous swing leg trajectory by using the concept of cubic polynomial and cubic spline interpolation. By applying these interpolatio...

In this paper, a class of singular two-point boundary value problems are solved using hybrid cubic B-spline method. algorithm, free parameter γ plays an important role to give accurate converge results for the solution. This chosen via optimization. Numerical examples displayed prove that our suggested method is flexible and effective, numerical compared with other methods from literature

Abstract In this paper, we give some basic concepts of q -calculus that will be needed in paper. Then, built the q-nonlocal condition ensures solution existence and uniqueness fractional q-integrodifferential equation. Also, introduce continuous dependence solution. We find numerical using finite-difference-Trapezoidal cubic B-spline-Trapezoidal methods. Finally, three examples to illustrate va...

Abstract: This study proposes new C rational cubic spline interpolant of the form cubic/quadratic with three shape parameters to preserves the geometric properties of the given data sets. Sufficient conditions for the positivity and data constrained modeling of the rational interpolant are derived on one parameter while the remaining two parameters can further be utilized to change and modify t...

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 m...

in this article, a numerical approximation to the solution of the newell-whitehead equation (nwe) and cauchy problem of ill-posed non-linear diffusion equation have been studied. the presented scheme is obtained by using the derivative of the cubic b-spline quasi-interpolation (bsqi) to approximate the spatial derivative of the dependent variable and first order forward difference to approximat...

In this piece of work, using three spatial grid points, we discuss a new two-level implicit cubic spline method of O(k + kh + h) for the solution of quasi-linear parabolic equation   , , , , xx x t u f x t u u u  , 0< x <1, t > 0 subject to appropriate initial and Dirichlet boundary conditions, where h > 0, k > 0 are grid sizes in space and time-directions, respectively. The cubic spline app...

In this paper, a collocation approach is employed for the solution of the one-dimensional telegraph equation based on cubic B-spline. The derived method leads to a tri-diagonal linear system. Computational efficiency of the method is confirmed through numerical examples whose results are in good agreement with theory. The obtained numerical results have been compared with the results obtained b...