In this paper, the effective computational method (ECM) based on the standard monomial polynomial has been implemented to solve the nonlinear Jeffery-Hamel flow problem. Moreover, novel effective computational methods have been developed and suggested in this study by suitable base functions, namely Chebyshev, Bernstein, Legendre, and Hermite polynomials. The utilization of the base functions converts the nonlinear problem to a nonlinear algebraic system of equations, which is then resolved using the Mathematica®12 program. The development of effective computational methods (D-ECM) has been applied to solve the nonlinear Jeffery-Hamel flow problem, then a comparison between the methods has been shown. Furthermore, the maximum error remainder ( ) has been calculated to exhibit the reliability of the suggested methods. The results persuasively prove that ECM and D-ECM are accurate, effective, and reliable in getting approximate solutions to the problem.
All modern critical approaches attempt to cover the meanings and overtones of the text, claiming that they are better than others in the analysis and attainment of the intended meanings of the text. The structural approach claims to be able to do so more than any other modern critical approach, as it claimed that it is possible to separate what is read from the reader, on the presumed belief that it is possible to read the text with a zero-memory. However, the studies in criticism of criticism state that each of these approaches is successful in dealing with the text in one or more aspects while failing in one or more aspects. Consequently, the criticism whether the approach possesses the text, or that the text rejects this possession, r
... Show MoreA theoretical analysis of mixing in the secondary combustion chamber of ramjet is presented. Theoretical investigations were initiated to insight into the flow field of the mixing zone of the ramjet combustor and a computer program to calculate axisymmetric, reacting and inert flow was developed. The mathematical model of the mixing zone of ramjet comprises differential equations for: continuity, momentum, stagnation enthalpy, concentration, turbulence energy and its dissipation rate. The simultaneous solution of these equations by means of a finite-difference solution algorithm yields the values of the variable at all internal grid nodes.
The results showed that increasing air mass flow (0.32 to 0.64 kg/s) increases the development o
هناك دائما حاجة إلى طريقة فعالة لتوليد حل عددي أكثر دقة للمعادلات التكاملية ذات النواة المفردة أو المفردة الضعيفة لأن الطرق العددية لها محدودة. في هذه الدراسة ، تم حل المعادلات التكاملية ذات النواة المفردة أو المفردة الضعيفة باستخدام طريقة متعددة حدود برنولي. الهدف الرئيسي من هذه الدراسة هو ايجاد حل تقريبي لمثل هذه المشاكل في شكل متعددة الحدود في سلسلة من الخطوات المباشرة. أيضا ، تم افتراض أن مقام النواة
... Show MoreThe aim of this paper is to propose a reliable iterative method for resolving many types of Volterra - Fredholm Integro - Differential Equations of the second kind with initial conditions. The series solutions of the problems under consideration are obtained by means of the iterative method. Four various problems are resolved with high accuracy to make evident the enforcement of the iterative method on such type of integro differential equations. Results were compared with the exact solution which exhibits that this technique was compatible with the right solutions, simple, effective and easy for solving such problems. To evaluate the results in an iterative process the MATLAB is used as a math program for the calculations.
Algorithms using the second order of B -splines [B (x)] and the third order of B -splines [B,3(x)] are derived to solve 1' , 2nd and 3rd linear Fredholm integro-differential equations (F1DEs). These new procedures have all the useful properties of B -spline function and can be used comparatively greater computational ease and efficiency.The results of these algorithms are compared with the cubic spline function.Two numerical examples are given for conciliated the results of this method.
in this paper the collocation method will be solve ordinary differential equations of retarted arguments also some examples are presented in order to illustrate this approach