Differential Equation 1.1

Differential Equation 1.1 - Numerical solution of...

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University of Virginia, MSE 4270/6270: Introduction to Atomistic Simulations, Leonid Zhigilei Deriving and solving differential equations (DE) is a common task in computational research. ¾ Many physical laws/relations are formulated in terms of DE. ¾ Most continuum simulation methods are based on solution of DE. Numerical solution of differential equations Although the finite difference and the finite element methods typically used to solve DE are often intuitively associated with large-scale macroscopic problems, this association is inadequate. The methods are not calibrated to any physical time or length scale. Numerical methods for solving DE is a vast and complex subject area. In this lecture we will only scratch the surface by briefly discussing several methods used for solving a system of ordinary DE relevant to Particle Dynamics methods.
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University of Virginia, MSE 4270/6270: Introduction to Atomistic Simulations, Leonid Zhigilei Particle Dynamics models: Physical system is represented as a sets of particles rather than densities (fields) evolving over time. Examples:
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Differential Equation 1.1 - Numerical solution of...

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