The paper deals with stiff systems of differential equations. To solve this sort of system numerically is a diffult task. In spite of the fact that we come across stiff systems quite often in the common practice, a very interesting and promissing numerical method of solving systems of ordinary differential equations (ODE) based on Taylor series has appeared. The question was how to harness the ...

In this study, by using the concepts of subordination, we define a new family RM,N,λ,γ starlike functions complex order γ connected with cardioid domain. The main contribution article consists derivations sharp inequality, considering belonging to in U. Particularly, bounds first two Taylor–Maclaurin coefficients, estimates Fekete–Szegö-type functionals, and coefficient inequalities are investi...

The motivation of the present article is to define (p−q)-Wanas operator in geometric function theory by symmetric nature quantum calculus. We also initiate and explore certain new families holormorphic bi-univalent functions AE(λ,σ,δ,s,t,p,q;ϑ) SE(μ,γ,σ,δ,s,t,p,q;ϑ) which are defined unit disk U associated with operator. upper bounds for initial Taylor–Maclaurin coefficients Fekete–Szegö-type i...

Abstract. The Euler-MacLaurin summation formula relates a sum of a function to a corresponding integral, with a remainder term. The remainder term has an asymptotic expansion, and for a typical analytic function, it is a divergent (Gevrey-1) series. Under some decay assumptions of the function in a half-plane (resp. in the vertical strip containing the summation interval), Hardy (resp. Abel-Pla...

The paper deals with stiff systems of differential equations. To solve this sort of system numerically is a diffult task. In spite of the fact that we come across stiff systems quite often in the common practice, a very interesting and promissing numerical method of solving systems of ordinary differential equations (ODE) based on Taylor series has appeared. The question was how to harness the ...

degenerate kernel approximation method is generalized to solve hammerstein system of fredholm integral equations of the second kind. this method approximates the system of integral equations by constructing degenerate kernel approximations and then the problem is reduced to the solution of a system of algebraic equations. convergence analysis is investigated and on some test problems, the propo...

In this paper we obtain certain generalizations of the trapezoidal rule and the Euler-Maclaurin formula that involve derivatives. In the case of quadrature of functions of exponential type over infinite intervals we find conditions under which existence of the (improper) integral and convergence of the approximating series become equivalent. In the process, we also establish a best possible ver...

In this study, it has been researched the exponential curve as a $3^{rd},$ $5^{th}$ and $7^{th}$ order B\'{e}zier in $\mathbf{E}^{2}$. Also, numerical matrix representations of these curves have calculated using Maclaurin series plane via control points.