Class: Cash_Karp_RK4

Inherits:
Object
  • Object
show all
Includes:
Integrator
Defined in:
lib/integrator/rkck.rb

Direct Known Subclasses

Adaptive_Cash_Karp_RK45

Constant Summary collapse

A2 = 
0.2
A3 = 
0.3
A4 = 
0.6
A5 = 
1.0
A6 = 
0.875
B21 = 
0.2
B31 = 
3.0/40.0
B32 = 
9.0/40.0
B41 = 
0.3
B42 = 
-0.9
B43 = 
1.2
B51 = 
-11.0/54.0
B52 = 
2.5
B53 = 
-70.0/27.0
B54 = 
35.0/27.0
B61 = 
1631.0/55296.0
B62 = 
175.0/512.0
B63 = 
575.0/13824.0
B64 = 
44275.0/110592.0
B65 = 
253.0/4096.0
C1 = 
37.0/378.0
C3 = 
250.0/621.0
C4 = 
125.0/594.0
C6 = 
512.0/1771.0
DC1 = 
C1-2825.0/27648.0
DC3 = 
C3-18575.0/48384.0
DC4 = 
C4-13525.0/55296.0
DC5 = 
-277.00/14336.0
DC6 = 
C6-0.25

Instance Method Summary collapse

Methods included from Integrator

#Integrator_initialize, #integrate, #set_max_samples

Constructor Details

#initialize ⇒ Cash_Karp_RK4

Returns a new instance of Cash_Karp_RK4.



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# File 'lib/integrator/rkck.rb', line 50

def initialize
  Integrator_initialize()
end

Instance Method Details

#integrate_fixed_step(y, dydx, x, h, derivs) ⇒ Object 



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# File 'lib/integrator/rkck.rb', line 54

def integrate_fixed_step(y, dydx, x, h, derivs)
  raise "Bad type!" unless [y, dydx].all? { |var| var.kind_of?(Vector) }
  raise "Bad type!" unless [x, h].all? { |var| var.kind_of?(Float) }
  raise "Bad method!" unless derivs.kind_of?(Proc)

  ytemp = y + dydx * B21 * h
  ak2 = derivs.call(x + A2*h, ytemp)
  ytemp = y + (dydx * B31 + ak2 * B32) * h
  ak3 = derivs.call(x + A3*h, ytemp)
  ytemp = y + (dydx * B41 + ak2 * B42 + ak3 * B43) * h
  ak4 = derivs.call(x + A4*h, ytemp)
  ytemp = y + (dydx * B51 + ak2 * B52 + ak3 * B53 + ak4 * B54) * h
  ak5 = derivs.call(x + A5*h, ytemp)
  ytemp = y + (dydx * B61 + ak2 * B62 + ak3 * B63 + ak4 * B64 +
 ak5 * B65) * h
  ak6 = derivs.call(x + A6*h, ytemp)
  yout = y + (dydx * C1 + ak3 * C3 + ak4 * C4 + ak6 * C6) * h
  yerr = (dydx * DC1 + ak3 * DC3 + ak4 * DC4 + ak5 * DC5 + ak6 * DC6) * h

  # Return new values and error terms
  [yout, yerr]
end