Leapfrog Algorithm

1
Leapfrog Algorithm
http//www.math.iastate.edu/wu/math597.html
http//www.math.iastate.edu/wu/Math597HW0000

• Math/BCB/ComS597
• Zhijun Wu
• Department of Mathematics

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Newtons Equations
3
Reducing to First Order
4
Numerical Solution
x
v
x(t)
v(t)
xk1
xk
vk1
vk
t
t
tk
tk1
tk
tk1
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Leapfrog Algorithm
vk-1/2
vk1/2
xk-1
xk
xk1
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A Simple Example
potential energy
h (x)
h(x)
x
force field
7
Newtons Equation
h (x)
h(x)
x
8
Systems of Equations
h (x)
h(x)
x
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Numerical Algorithm
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x (t), x1 1, v1/2 0.5, ?t 0.02