Matrix Exponentiation and the Frank-Kamenetskii Equation
نویسندگان
چکیده
Long time solutions to the Frank-Kamenetskii partial differential equation modelling a thermal explosion in a vessel are obtained using matrix exponentiation. Spatial derivatives are approximated by high-order finite difference approximations. A forward difference approximation to the time derivative leads to a Lawson-Euler scheme. Computations performed with a BDF approximation to the time derivative and a fourth-order Runge-Kutta approximation to the time derivative are compared to results obtainedwith the Lawson-Euler scheme. Variation in the central temperature of the vessel corresponding to changes in the shape parameter and Frank-Kamenetskii parameter are computed and discussed.
منابع مشابه
Numerical Simulation of the Frank-Kamenetskii PDE: GPU vs. CPU Computing
The efficient solution of the Frank-Kamenetskii partial differential equation through the implementation of parallelized numerical algorithms or GPUs (Graphics Processing Units) in MATLAB is a natural progressionof the workwhich has been conducted in an area of practical import. There is an on-going interest in the mathematics describing thermal explosions due to the significance of the applica...
متن کاملHopscotch method: The numerical solution of the Frank-Kamenetskii partial differential equation
Keywords: Hopscotch scheme Thermal explosion Nonlinear source term Linear stability analysis a b s t r a c t Numerical solutions to the Frank-Kamenetskii partial differential equation modelling a thermal explosion in a cylindrical vessel are obtained using the hopscotch scheme. We observe that a nonlinear source term in the equation leads to numerical difficulty and hence adjust the scheme to a...
متن کاملAnalytical approach to initiation of propagating fronts.
We consider the problem of initiation of a propagating wave in a one-dimensional bistable or excitable fiber. In the Zeldovich-Frank-Kamenetskii equation, also known as the Nagumo equation and Schlögl model, the key role is played by the "critical nucleus" solution whose stable manifold is the threshold surface separating initial conditions leading to the initiation of propagation and decay. An...
متن کاملValery (Chrom) Ivanov in memoriam.
Valery (Chrom) Ivanov In memoriam Maxim Frank-Kamenetskii a , Edward Trifonov b , Victor Zhurkin c , Victor Danilov d , Mukti Sarma e & Ramaswamy Sarma e a Department of Biomedical Engineering, Boston University, Boston, MA, USA b Institute of Evolution, University of Haifa, Haifa, Israel c National Cancer Institute, Bethesda, MD, USA d Institute of Molecular Biology and Genetics of National Ac...
متن کاملEfficient elliptic curve cryptosystems
Elliptic curve cryptosystems (ECC) are new generations of public key cryptosystems that have a smaller key size for the same level of security. The exponentiation on elliptic curve is the most important operation in ECC, so when the ECC is put into practice, the major problem is how to enhance the speed of the exponentiation. It is thus of great interest to develop algorithms for exponentiation...
متن کامل