Where initial values of the dependent variables are: 𝑥 𝑖  𝑡 0  = 𝛼 𝑖, 𝛼 𝑖 = c o n s t. Then, we focus on the poisons, including xenon135 and samarium-149, burnups in a suggested 1000 MWe PWR as well as its plutonium isotopes build up. First we explain Muon Catalyzed Fusion ( 𝜇CF) and find the fusion cycling rate. Therefore, in the present study, some dynamical problems (which mathematically are coupled first-order IVPs) are studied as examples of the present solver ability. The main aim of the present research is to give a MATLAB-linked solver to solve first-order coupled differential equation which is used in many subjects of the nuclear engineering. The well-known numerical methods such as Runge-Kutta, Rosenbrock, Classical method, Taylor series, Adams-Bashforth are used to solve IVPs using our MATLAB-linked solver. In our early studies, we have utilized a numerical “MATLAB-linked solver” to calculate stiff or nonstiff first-order coupled IVPs using MATLAB software, and reader can find these programs in the appendix.
#How to define unknown variables in matlab 2009 software#
It is possible to describe many dynamical problems using IVPs MATLAB is the best software for engineers and applied scientists to solve the problems numerically, specially solving IVPs.
IntroductionĬoupled first-order IVPs are frequently used in many parts of engineering and sciences, and we presented a package seems to be useful for researchers to solve IVPs. Then, we have focused on the fuel depletion in a suggested PWR including poisons burnups (xenon-135 and samarium-149), plutonium isotopes production, and uranium depletion. Muon catalyzed fusion in a D-T mixture is considered as a first dynamical example of the coupled IVPs. Some applications related to IVPs are given here using our MATLAB-linked solver. We present a “solver” including three computer programs which were joint with the MATLAB software to solve and plot solutions of the first-order coupled stiff or nonstiff IVPs. Coupled first-order IVPs are frequently used in many parts of engineering and sciences.
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