It is well known that the complex step method is a tool that calculates derivatives by imposing a complex step in a strict sense. We extended the method by employing the fractional calculus differential operator in this paper. The fractional calculus can be taken in the sense of the Caputo operator, Riemann-Liouville operator, and so forth. Furthermore, we derived several approximations for com...

We have learned that the numerical solution obtained from Euler's method, converges to the exact solution () of the initial value problem ′ = (,), (0) = 0 , as ℎ → 0. We now analyze the convergence of a general one-step method of the form +1 = + ℎΦ(, , ℎ), for some continuous function Φ(, , ℎ). We define the local truncation error of this one-step method by (ℎ) = (+1) − () ℎ − Φ(, (), ℎ). That ...

The Lax-Friedrichs (LxF) method [2, 3, 4] is a basic method for the solution of hyperbolic partial differential equations (PDEs). Its use is limited because its order is only one, but it is easy to program, applicable to general PDEs, and has good qualitative properties because it is monotone. The LxF method is often used to show the effects of dissipation, but it is not actually a dissipative ...

Differentiation of members of the Mycobacterium tuberculosis complex by conventional mycobacteriological methods is time consuming, making surveillance of species-specific disease difficult. A two-step, multiplex polymerase chain reaction (PCR) method based on genomic regions of difference (RD1, RD1(mic), RD2(seal), RD4, RD9 and RD12) was developed for the differentiation of M. canettii, M. tub...

Salmonella enterica serovar Pullorum/Gallinarum is an important infectious pathogen that has caused widespread problems for chicken industry. Traditional Salmonella serotyping is an expensive and time-consuming process. In this study, we developed a rapid one-step polymerase chain reaction (PCR) method to identify S. Pullorum/Gallinarum. The PCR-based assay focuses on flhB, which shows a defici...

We developed a nested, multiplex PCR for simultaneous detection of three species of chlamydiae in human and avian specimens. The PCR was designed to increase sensitivity and to circumvent inhibitors of PCR present in clinical specimens. The target sequence was the 16S rRNA gene. The first-step PCR was genus specific, and the second-step PCR was multiplexed (i.e., had multiple primer sets in the...

BACKGROUND Genes for human epidermal growth factor receptors B1 (ErbB1) and B2 (ErbB2) were amplified in breast and ovarian cancers. Both of them were associated with aggressive disease and worse prognosis. The ErbB1 or ErbB2 status of a tumor may provide an indication of the response to ErbB1 and ErbB2 -targeted therapies. For accurate and rapid assessment of amplification of ErbB1 and ErbB2 o...