Question

State the conditions on the nodes, weights and matrix of an explicit 2-stage RK method of order

2. Give an example of such a method (in a form of a tableaux).

Answer 1

An explicit 2-stage RK method of order 2 requires certain conditions on the nodes, weights, and matrix. Here is an example of such a method in tableaux form.

Step-by-step explanation:

Explicit 2-Stage RK Method of Order 2

An explicit 2-stage Runge-Kutta (RK) method of order 2 requires certain conditions on the nodes, weights, and matrix. The nodes must be chosen such that the method is explicit, meaning the matrix of coefficients is lower triangular. The weights must satisfy certain conditions related to the Taylor expansion of the solution. The matrix must be chosen such that the method has order 2, which means it accurately approximates the solution to second-order differential equations.

Here is an example of an explicit 2-stage RK method in tableaux form:

+---+---+---+
| 0 | | |
| 1 | 1 | |
+---+---+---+
| 1/2 | 1/2 | |
+---+---+---+