Solving differential equations
6 important questions on Solving differential equations
What is the difference between an analytical solution and a numerical solution?
How do we solve numerical solutions?
What is the goal of solving an equation?
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What are the steps to solve an analytical equation?
- Goal: N(t) = ....
- 1. Divide both sides by N
- 2. Integrate both sides with respect to t
- 3. Left side: simplify to N. Right side: integrate
- 4. Left side: determine integral
- 5. Solve equation for N(t)
- 6. Use initial conditions to find a value for the integration constant
What is the forward euler method
The Euler method is a first-order method, which means that the local error (error per step) is proportional to the square of the step size, and the global error (error at a given time) is proportional to the step size. The Euler method often serves as the basis to construct more complex methods
N(t + delta t) = N(t) + delta t * (delta N / delta t)
How can you make more accurate predictions with the euler method?
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