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Lecture

Numerical Solution Methods

In course

CH-310: Dynamics and kinetics

The course covers the principles of chemical kinetics, including differential rate laws, derivation of exact and approximate integral rate laws for common elementary and composite reactions, fundamentals of collision and transition state theories, and appl ...

Description

This lecture covers numerical solution methods for dynamics and kinetics, focusing on solving rate equations and first-order reversible reactions using stochastic methods. The instructor explains the process step by step, from defining the rate constants to simulating the reactions over time.

Instructor

Ulrich Lorenz

Official source

Related concepts (28)

Rate equation

In chemistry, the rate law or rate equation for a chemical reaction is a mathematical equation that links the rate of forward reaction with the concentrations or pressures of the reactants and constant parameters (normally rate coefficients and partial reaction orders). For many reactions, the initial rate is given by a power law such as where [\mathrm{A}] and [\mathrm{B}] express the concentration of the species \mathrm{A} and \mathrm{B}, usually in moles per liter (molarity, M).

Numerical analysis

Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of numerical methods that attempt at finding approximate solutions of problems rather than the exact ones. Numerical analysis finds application in all fields of engineering and the physical sciences, and in the 21st century also the life and social sciences, medicine, business and even the arts.

Numerical methods for ordinary differential equations

Numerical methods for ordinary differential equations are methods used to find numerical approximations to the solutions of ordinary differential equations (ODEs). Their use is also known as "numerical integration", although this term can also refer to the computation of integrals. Many differential equations cannot be solved exactly. For practical purposes, however – such as in engineering – a numeric approximation to the solution is often sufficient. The algorithms studied here can be used to compute such an approximation.

Numerical methods for partial differential equations

Numerical methods for partial differential equations is the branch of numerical analysis that studies the numerical solution of partial differential equations (PDEs). In principle, specialized methods for hyperbolic, parabolic or elliptic partial differential equations exist. Finite difference method In this method, functions are represented by their values at certain grid points and derivatives are approximated through differences in these values.

Reaction rate

The reaction rate or rate of reaction is the speed at which a chemical reaction takes place, defined as proportional to the increase in the concentration of a product per unit time and to the decrease in the concentration of a reactant per unit time. Reaction rates can vary dramatically. For example, the oxidative rusting of iron under Earth's atmosphere is a slow reaction that can take many years, but the combustion of cellulose in a fire is a reaction that takes place in fractions of a second.

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Basic Concepts of Kinetics: Reactions and Rate Constants

Covers the basic concepts of kinetics, including reaction mechanisms and rate laws.

Macroscopic Kinetics: Reaction Dynamics & Integrated Rate Laws

Covers macroscopic kinetics, reaction dynamics, rate equations, stochiometric coefficients, and integrated rate laws.

Stochastic Method: Kinetics Modeling