diff options
Diffstat (limited to 'src/vZ')
| -rw-r--r-- | src/vZ/BS23.hpp | 20 | ||||
| -rw-r--r-- | src/vZ/Euler.hpp | 2 | ||||
| -rw-r--r-- | src/vZ/HE12.hpp | 14 | ||||
| -rw-r--r-- | src/vZ/Heun.hpp | 6 | ||||
| -rw-r--r-- | src/vZ/Midpoint.hpp | 6 | ||||
| -rw-r--r-- | src/vZ/RK4.hpp | 8 |
6 files changed, 17 insertions, 39 deletions
diff --git a/src/vZ/BS23.hpp b/src/vZ/BS23.hpp index 1092d81..f81cad1 100644 --- a/src/vZ/BS23.hpp +++ b/src/vZ/BS23.hpp @@ -23,20 +23,18 @@ namespace vZ { - // Heun-Euler method + // Bogacki-Shampine method // - // Second-order with embedded first-order + // Third-order with embedded second-order // Its tableau is: // - // 0 | - // 1 | 1 - // --+--------- - // | 1/2 1/2 - // | 1 0 - // - // k1 = dt*f(y[n]) - // k2 = dt*f(y[n] + dt*k1) - // y[n + 1] = y[n] + 1/2*(k1 + k2) + // 0 | + // 1/2 | 1/2 + // 3/4 | 0 3/4 + // 1 | 2/9 1/3 4/9 + // ----+----------------- + // b | 2/9 1/3 4/9 0 + // b* | 7/24 1/4 1/3 1/8 template <typename Y> class GenericBS23Integrator : public GenericAdaptiveIntegrator<Y> { diff --git a/src/vZ/Euler.hpp b/src/vZ/Euler.hpp index 033da2e..ba53b98 100644 --- a/src/vZ/Euler.hpp +++ b/src/vZ/Euler.hpp @@ -32,8 +32,6 @@ namespace vZ // 0 | // --+-- // | 1 - // - // y[n + 1] = y[n] + dt*f(y[n]) template <typename Y> class GenericEulerIntegrator : public GenericSimpleIntegrator<Y> { diff --git a/src/vZ/HE12.hpp b/src/vZ/HE12.hpp index 0f7a299..48d63ec 100644 --- a/src/vZ/HE12.hpp +++ b/src/vZ/HE12.hpp @@ -28,15 +28,11 @@ namespace vZ // Second-order with embedded first-order // Its tableau is: // - // 0 | - // 1 | 1 - // --+--------- - // | 1/2 1/2 - // | 1 0 - // - // k1 = dt*f(y[n]) - // k2 = dt*f(y[n] + dt*k1) - // y[n + 1] = y[n] + 1/2*(k1 + k2) + // 0 | + // 1 | 1 + // ---+--------- + // b | 1/2 1/2 + // b* | 1 0 template <typename Y> class GenericHE12Integrator : public GenericAdaptiveIntegrator<Y> { diff --git a/src/vZ/Heun.hpp b/src/vZ/Heun.hpp index 5e697af..7de2f40 100644 --- a/src/vZ/Heun.hpp +++ b/src/vZ/Heun.hpp @@ -32,11 +32,7 @@ namespace vZ // 0 | // 1 | 1 // --+--------- - // | 1/2 1/2 - // - // k1 = dt*f(y[n]) - // k2 = dt*f(y[n] + dt*k1) - // y[n + 1] = y[n] + 1/2*(k1 + k2) + // b | 1/2 1/2 template <typename Y> class GenericHeunIntegrator : public GenericSimpleIntegrator<Y> { diff --git a/src/vZ/Midpoint.hpp b/src/vZ/Midpoint.hpp index a4bb906..071e589 100644 --- a/src/vZ/Midpoint.hpp +++ b/src/vZ/Midpoint.hpp @@ -32,11 +32,7 @@ namespace vZ // 0 | // 1/2 | 1/2 // ----+------ - // | 0 1 - // - // k1 = dt*f(y[n]) - // k2 = dt*f(y[n] + (dt/2)*k1) - // y[n + 1] = y[n] + k2 + // b | 0 1 template <typename Y> class GenericMidpointIntegrator : public GenericSimpleIntegrator<Y> { diff --git a/src/vZ/RK4.hpp b/src/vZ/RK4.hpp index 39fa306..0eb680e 100644 --- a/src/vZ/RK4.hpp +++ b/src/vZ/RK4.hpp @@ -34,13 +34,7 @@ namespace vZ // 1/2 | 0 1/2 // 1 | 0 0 1 // ----+---------------- - // | 1/6 1/3 1/3 1/6 - // - // k1 = dt*f(y[n]) - // k2 = dt*f(y[n] + (dt/2)*k1) - // k3 = dt*f(y[n] + (dt/2)*k2) - // k4 = dt*f(y[n] + dt*k3) - // y[n + 1] = y[n] + (k1 + 2*k2 + 2*k3 + k4)/6 + // b | 1/6 1/3 1/3 1/6 template <typename Y> class GenericRK4Integrator : public GenericSimpleIntegrator<Y> { |