Is there a database/website with Butcher tableaus?












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I have started investigating in mostly Runge Kutta and Runge Kutta Nyström methods and there one of the only differences between the methods of the same type is their Butcher tableu. For the most common ones (RK4, RKF45, DOPRI54) they can be found on Wikipedia but otherwise I find it hard to find them. I could always go back the original paper but it can be a bit complicated for a newbie like me to read and understand. For example the Tsistouras 5 integrator. It seems unnecessary if people have to do all that work everytime to get those. Is there any website that has a larger collection of butcher tableus?






ode runge-kutta







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    2












    $begingroup$


    I have started investigating in mostly Runge Kutta and Runge Kutta Nyström methods and there one of the only differences between the methods of the same type is their Butcher tableu. For the most common ones (RK4, RKF45, DOPRI54) they can be found on Wikipedia but otherwise I find it hard to find them. I could always go back the original paper but it can be a bit complicated for a newbie like me to read and understand. For example the Tsistouras 5 integrator. It seems unnecessary if people have to do all that work everytime to get those. Is there any website that has a larger collection of butcher tableus?






    ode runge-kutta







    share|cite|improve this question











    $endgroup$















      2












      2








      2





      $begingroup$


      I have started investigating in mostly Runge Kutta and Runge Kutta Nyström methods and there one of the only differences between the methods of the same type is their Butcher tableu. For the most common ones (RK4, RKF45, DOPRI54) they can be found on Wikipedia but otherwise I find it hard to find them. I could always go back the original paper but it can be a bit complicated for a newbie like me to read and understand. For example the Tsistouras 5 integrator. It seems unnecessary if people have to do all that work everytime to get those. Is there any website that has a larger collection of butcher tableus?






      ode runge-kutta







      share|cite|improve this question











      $endgroup$




      I have started investigating in mostly Runge Kutta and Runge Kutta Nyström methods and there one of the only differences between the methods of the same type is their Butcher tableu. For the most common ones (RK4, RKF45, DOPRI54) they can be found on Wikipedia but otherwise I find it hard to find them. I could always go back the original paper but it can be a bit complicated for a newbie like me to read and understand. For example the Tsistouras 5 integrator. It seems unnecessary if people have to do all that work everytime to get those. Is there any website that has a larger collection of butcher tableus?






      ode runge-kutta




      ode runge-kutta






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      share|cite|improve this question













      share|cite|improve this question




      share|cite|improve this question








      edited 1 hour ago









      GertVdE

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      5,1551433










      asked 2 hours ago









      Hugo GransträmHugo Gransträm

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      405






















          1 Answer
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          $begingroup$

          The three best sources of Butcher tableaus are, according to me, the reference books





          • Numerical Methods for Ordinary Differential Equations, 3rd ed., J.C. Butcher,


          • Solving Ordinary Differential Equations I, 2nd ed., Hairer, Norsett and Wanner and


          • Solving Ordinary Differential Equations II, 2nd ed., Hairer and Wanner.


          You will have to browse through the books but all three of them contain a huge number of tableaus with indications of the "method name" (like Dormand-Prince). Unfortunately, the Butcher book has a very limited index so you'll really need to browse the book.



          There is also a comprehensive list on Wikipedia.



          The Julia language extension DifferentialEquations.jl also has a large set of tableaus implemented. You can find the implementation of the tableaus here.






          share|cite|improve this answer











          $endgroup$













          • $begingroup$
            Exactly what I looked for ;-). Thank you very much :-D
            $endgroup$
            – Hugo Gransträm
            1 hour ago












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          1 Answer
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          1 Answer
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          active

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          $begingroup$

          The three best sources of Butcher tableaus are, according to me, the reference books





          • Numerical Methods for Ordinary Differential Equations, 3rd ed., J.C. Butcher,


          • Solving Ordinary Differential Equations I, 2nd ed., Hairer, Norsett and Wanner and


          • Solving Ordinary Differential Equations II, 2nd ed., Hairer and Wanner.


          You will have to browse through the books but all three of them contain a huge number of tableaus with indications of the "method name" (like Dormand-Prince). Unfortunately, the Butcher book has a very limited index so you'll really need to browse the book.



          There is also a comprehensive list on Wikipedia.



          The Julia language extension DifferentialEquations.jl also has a large set of tableaus implemented. You can find the implementation of the tableaus here.






          share|cite|improve this answer











          $endgroup$













          • $begingroup$
            Exactly what I looked for ;-). Thank you very much :-D
            $endgroup$
            – Hugo Gransträm
            1 hour ago
















          2












          $begingroup$

          The three best sources of Butcher tableaus are, according to me, the reference books





          • Numerical Methods for Ordinary Differential Equations, 3rd ed., J.C. Butcher,


          • Solving Ordinary Differential Equations I, 2nd ed., Hairer, Norsett and Wanner and


          • Solving Ordinary Differential Equations II, 2nd ed., Hairer and Wanner.


          You will have to browse through the books but all three of them contain a huge number of tableaus with indications of the "method name" (like Dormand-Prince). Unfortunately, the Butcher book has a very limited index so you'll really need to browse the book.



          There is also a comprehensive list on Wikipedia.



          The Julia language extension DifferentialEquations.jl also has a large set of tableaus implemented. You can find the implementation of the tableaus here.






          share|cite|improve this answer











          $endgroup$













          • $begingroup$
            Exactly what I looked for ;-). Thank you very much :-D
            $endgroup$
            – Hugo Gransträm
            1 hour ago














          2












          2








          2





          $begingroup$

          The three best sources of Butcher tableaus are, according to me, the reference books





          • Numerical Methods for Ordinary Differential Equations, 3rd ed., J.C. Butcher,


          • Solving Ordinary Differential Equations I, 2nd ed., Hairer, Norsett and Wanner and


          • Solving Ordinary Differential Equations II, 2nd ed., Hairer and Wanner.


          You will have to browse through the books but all three of them contain a huge number of tableaus with indications of the "method name" (like Dormand-Prince). Unfortunately, the Butcher book has a very limited index so you'll really need to browse the book.



          There is also a comprehensive list on Wikipedia.



          The Julia language extension DifferentialEquations.jl also has a large set of tableaus implemented. You can find the implementation of the tableaus here.






          share|cite|improve this answer











          $endgroup$



          The three best sources of Butcher tableaus are, according to me, the reference books





          • Numerical Methods for Ordinary Differential Equations, 3rd ed., J.C. Butcher,


          • Solving Ordinary Differential Equations I, 2nd ed., Hairer, Norsett and Wanner and


          • Solving Ordinary Differential Equations II, 2nd ed., Hairer and Wanner.


          You will have to browse through the books but all three of them contain a huge number of tableaus with indications of the "method name" (like Dormand-Prince). Unfortunately, the Butcher book has a very limited index so you'll really need to browse the book.



          There is also a comprehensive list on Wikipedia.



          The Julia language extension DifferentialEquations.jl also has a large set of tableaus implemented. You can find the implementation of the tableaus here.







          share|cite|improve this answer














          share|cite|improve this answer



          share|cite|improve this answer








          edited 1 hour ago

























          answered 1 hour ago









          GertVdEGertVdE

          5,1551433




          5,1551433












          • $begingroup$
            Exactly what I looked for ;-). Thank you very much :-D
            $endgroup$
            – Hugo Gransträm
            1 hour ago


















          • $begingroup$
            Exactly what I looked for ;-). Thank you very much :-D
            $endgroup$
            – Hugo Gransträm
            1 hour ago
















          $begingroup$
          Exactly what I looked for ;-). Thank you very much :-D
          $endgroup$
          – Hugo Gransträm
          1 hour ago




          $begingroup$
          Exactly what I looked for ;-). Thank you very much :-D
          $endgroup$
          – Hugo Gransträm
          1 hour ago


















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