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monty37
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why is the 4th order Runge -Kutta method widely used than the 2nd or 3rd,for
solving ordinary differential equations?
solving ordinary differential equations?
arildno said:Cost-effectiveness.
Although 2. and 3.order Runge-Kutta are quicker than 4th order, they are much less exact.
For orders higher than 4, those take too long time to compute.
On another note:
Although I won't vouch for at which order this will become significant, the upper limit of an approximate scheme in terms of exactness will be when the finite arithmetic of the computer starts messing with the answers we want.
matematikawan said:I agree with you. Just that I never see RK3 formula in the literatures . Why is that so?
A solution to an ordinary differential equation is a function that satisfies the given equation and its initial conditions. It represents the relationship between a dependent variable and an independent variable.
A solution to an ordinary differential equation is a specific function that satisfies the given equation and initial conditions, while a general solution is a family of solutions that includes all possible solutions to the equation. A general solution may contain arbitrary constants that can be determined by applying the initial conditions.
Initial conditions are values given for the dependent variable and its derivatives at a specific point. They are important because they help determine the specific solution to an ordinary differential equation from a general solution.
The steps involved in finding a solution to an ordinary differential equation are:
No, not all ordinary differential equations can be solved analytically, especially for more complex equations. In some cases, numerical methods or approximations are used to find a solution.