A hybrid algorithm for coupling partial differential equation and compartment-based dynamics
نویسندگان
چکیده
منابع مشابه
A hybrid algorithm for coupling partial differential equation and compartment-based dynamics
Stochastic simulation methods can be applied successfully to model exact spatio-temporally resolved reaction-diffusion systems. However, in many cases, these methods can quickly become extremely computationally intensive with increasing particle numbers. An alternative description of many of these systems can be derived in the diffusive limit as a deterministic, continuum system of partial diff...
متن کاملA hybrid algorithm for coupling PDE and compartment-based dynamics
A hybrid algorithm for coupling PDE and compartment-based dynamics Jonathan U. Harrison a) and Christian A. Yates b) Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford, OX2 6GG, United Kingdom Department of Mathematical Sciences, University of Bath, Claverton Down, Bath, BA2 7AY, Uni...
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Spatial reaction-diffusion models have been employed to describe many emergent phenomena in biological systems. The modelling technique most commonly adopted in the literature implements systems of partial differential equations (PDEs), which assumes there are sufficient densities of particles that a continuum approximation is valid. However, owing to recent advances in computational power, the...
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در این رساله به بررسی رفتار جواب های رده ای از معادلات دیفرانسیل با مشتقات جزیی در دامنه های کراندار می پردازیم . این معادلات به فرم نیم-خطی و غیر خطی برای مسایل مستقیم و معکوس مورد مطالعه قرار می گیرند . به ویژه، تاثیر شرایط مختلف فیزیکی را در مساله، نظیر وجود موانع و منابع، پراکندگی و چسبندگی در معادلات موج و گرما بررسی می کنیم و به دنبال شرایطی می گردیم که متضمن وجود سراسری یا عدم وجود سراسر...
A Compact Scheme for a Partial Integro-Differential Equation with Weakly Singular Kernel
Compact finite difference scheme is applied for a partial integro-differential equation with a weakly singular kernel. The product trapezoidal method is applied for discretization of the integral term. The order of accuracy in space and time is , where . Stability and convergence in norm are discussed through energy method. Numerical examples are provided to confirm the theoretical prediction ...
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ژورنال
عنوان ژورنال: Journal of The Royal Society Interface
سال: 2016
ISSN: 1742-5689,1742-5662
DOI: 10.1098/rsif.2016.0335