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25 //
26 // G4BogackiShampine45
27 //
28 // Class description:
29 //
30 // An implementation of the embedded RK method from the following paper
31 // by P. Bogacki and L. F. Shampine:
32 // "An efficient Runge-Kutta (4,5) pair"
33 // Comput. Math. with Appl., vol. 32, no. 6, pp. 15-28, Sep. 1996.
34 //
35 // An interpolation method provides the value of an intermediate
36 // point in a step -- if a step was sucessful.
37 //
38 // This version can provide the FSAL property of the method,
39 // which allows the reuse of the last derivative in the next step,
40 // but only by using the additional method GetLastDyDx() (an alternative
41 // interface for simpler use of FSAL is under development).
42
43 // Created: Somnath Banerjee, Google Summer of Code 2015, 25 May 2015
44 // Supervision: John Apostolakis, CERN
45 // --------------------------------------------------------------------
46 #ifndef BOGACKI_SHAMPINE_45_HH
47 #define BOGACKI_SHAMPINE_45_HH
48
49 #include "G4MagIntegratorStepper.hh"
50
51 class G4BogackiShampine45 : public G4MagIntegratorStepper
52 {
53 public:
54
55 G4BogackiShampine45(G4EquationOfMotion* EqRhs,
56 G4int numberOfVariables = 6,
57 G4bool primary = true);
58 ~G4BogackiShampine45() override;
59
60 G4BogackiShampine45(const G4BogackiShampine45&) = delete;
61 G4BogackiShampine45& operator=(const G4BogackiShampine45&) = delete;
62
63 void Stepper( const G4double y[],
64 const G4double dydx[],
65 G4double h,
66 G4double yout[],
67 G4double yerr[] ) override ;
68
69 // This Stepper provides 'dense output'. After a successful
70 // step, it is possible to obtain an estimate of the value
71 // of the function at an intermediate point of the interval.
72 // This requires only two additional evaluations of the
73 // derivative (and thus the field).
74
75 inline void SetupInterpolation()
76 {
77 SetupInterpolationHigh(); // ( yInput, dydx, Step);
78 }
79
80 // For calculating the output at the tau fraction of Step
81 //
82 inline void Interpolate( G4double tau,
83 G4double yOut[] ) // Output value
84 {
85 InterpolateHigh( tau, yOut);
86 // InterpolateHigh( yInput, dydx, Step, yOut, tau);
87 }
88
89 void SetupInterpolationHigh();
90
91 // For calculating the output at the tau fraction of Step
92 //
93 void InterpolateHigh( G4double tau,
94 G4double yOut[] ) const;
95
96 G4double DistChord() const override;
97 G4int IntegratorOrder() const override { return 4; }
98
99 void GetLastDydx( G4double dyDxLast[] );
100
101 void PrepareConstants(); // Initialise the values of the bi[][] array
102
103 private:
104
105 G4double *ak2, *ak3, *ak4, *ak5, *ak6, *ak7, *ak8,
106 *ak9, *ak10, *ak11, *yTemp, *yIn;
107
108 G4double *p[6];
109
110 G4double fLastStepLength = -1.0;
111 G4double *fLastInitialVector, *fLastFinalVector, *fLastDyDx,
112 *fMidVector, *fMidError;
113 // For DistChord calculations
114
115 G4BogackiShampine45* fAuxStepper = nullptr;
116 // For chord - until interpolation is proven
117 G4bool fPreparedInterpolation = false;
118
119 // Class constants
120 static G4bool fPreparedConstants;
121 static G4double bi[12][7];
122 };
123
124 #endif
125