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Runge–Kutta ray tracing technique for solving radiative …
https://www.sciencedirect.com/science/article/pii/S0022407315300649
Runge–Kutta methods - Wikipedia
https://en.wikipedia.org/wiki/Runge%E2%80%93Kutta_methods
In numerical analysis, the Runge–Kutta methods ( English: / ˈrʊŋəˈkʊtɑː / ( listen) RUUNG-ə-KUUT-tah) are a family of implicit and explicit iterative methods, which include the Euler method, used in temporal discretization for the approximate solutions of simultaneous non linear equations.
Runge-Kutta Ray Tracing Technique for Solving Radiative …
https://www.researchgate.net/publication/295539985_Runge-Kutta_Ray_Tracing_Technique_for_Solving_Radiative_Heat_Transfer_in_a_Two-Dimensional_Graded-Index_Medium
The curved ray trajectory in GIM is usually numerically solved by approximation method. Runge-Kutta ray tracing (RKRT) method developed by Huang et al. [29] has been proved to be simple in...
Runge–Kutta Ray-Tracing Technique for Radiative Transfer in a …
https://arc.aiaa.org/doi/10.2514/1.T5360
The Runge–Kutta ray-tracing method is combined with the Monte Carlo method to analyze the radiative transfer in a three-dimensional graded-index media. The analytical solution of the trajectory of a ray in a refractive index distribution of a Maxwell fisheye lens is obtained.
Runge-Kutta ray tracing technique for solving radiative heat …
https://ui.adsabs.harvard.edu/abs/2016JQSRT.176...24H/abstract
To improve the computational speed, the variable step-size Runge-Kutta ray tracing method is proposed, and the maximum relative error between the temperature field in the nonscattering medium by this method and the benchmark solution is less than 0.5%.
Reverse Monte Carlo coupled with Runge-Kutta ray …
https://www.sciencedirect.com/science/article/pii/S1350449519300908
In RMCRKRT, the Runge-Kutta ray tracing technique is employed to obtain the ray trajectory numerical solution of graded index medium, and the Reverse Monte Carlo method is employed to solve the radiative heat transfer problems. The correctness and accuracy of RMCRKRT is validated by comparing with the benchmark numerical solutions.
Reverse Monte Carlo coupled with Runge-Kutta ray …
https://www.researchgate.net/publication/332186682_Reverse_Monte_Carlo_coupled_with_Runge-Kutta_ray_tracing_method_for_radiative_heat_transfer_in_graded-index_media
In RMCRKRT, the Runge-Kutta ray tracing technique is employed to obtain the ray trajectory numerical solution of graded index medium, and the Reverse Monte Carlo method is employed to solve the...
Runge-Kutta method - Oklahoma State University–Stillwater
https://math.okstate.edu/people/yqwang/teaching/math4513_fall11/Notes/rungekutta.pdf
Here’s the formula for the Runge-Kutta-Fehlberg method (RK45). w 0 = k 1 = hf(t i;w i) k 2 = hf t i + h 4;w i + k 1 4 k 3 = hf t i + 3h 8;w i + 3 32 k 1 + 9 32 k 2 k 4 = hf t i + 12h 13;w i + 1932 2197 k 1 7200 2197 k 2 + 7296 2197 k 3 k 5 = hf t i +h;w i + 439 216 k 1 8k 2 + 3680 513 k 3 845 4104 k 4 k 6 = hf t i + h 2;w i 8 27 k 1 +2k 2 ...
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