Sharif Digital Repository

Ordinary frequently occur as mathematical models in many fields of science, engineering, differential equations (ODEs) and economy. It is rarely that ODEs have closed form analytical solutions, so it is common to seek approximate solutions by means of numerical methods. One of the most useful methods for the solution of ODEs is multi-step methods. Although the existing multi-step methods such as Adams—Moulton are accurate and useful, they also have their own limitations such as instability at large step sizes or weak performance in the case of stiff ODEs. Thus, multi-step methods that show better behavior compared to the existing methods are preferred, because they decrease the computational... 

In this paper, a novel multi-step method is proposed for solving the inverse point kinetics problem using Lagrange polynomial method. By use of this approach, the need for nuclear power history or the Laplace transform is vanished. Furthermore, the accuracy of the method is of order hn for the (n + 1)-point formula, where h is the computational time-step. The three- and five-point formulas of the Lagrange method are used for on-line reactivity calculations and results are benchmarked against reference solutions for different nuclear power forms. Moreover, results for different computational time-steps are compared in each case. The results show the accuracy of the proposed method in all... 

An environmentally friendly heterogeneous ternary carbon dots (CDs)/MIL-88B (Fe)/Bi2S3 nanocomposite was synthesized by a multistep method. In this study, we have studied low-temperature calcination with relatively inexpensive reactants. The sufficient CD arrays were generated by loading the glucose molecules into the pores of an as-obtained metal-organic framework (MOF), i.e. MIL-88B (Fe)), by heating to 200 °C. Fabricated nanocomposite structures were characterized by FT-IR, XRD, EIS, SEM, TEM, BET, and TGA techniques, demonstrating the decoration of the Bi2S3 on the CDs/MIL-88B (Fe) nanocomposite surface. MOF templating has been chosen as a systemic method for limited size CD formation...