Solving Equations Numerically
- To find the root of a graph, find the point where the graph passes through the x-axis – look for a sign change.
- Carry out a decimal search:
- Substitute the values between where a sign change has occurred.
- The closer to zero, the greater the accuracy.
- To solve the equation f(x) = 0, you can rearrange f(x) into a form x = …
- This function represents a sequence that starts at x0, moving to xr
- Substitute a value for x0 and put it into the function to get x1, and so on.
- As you increase r, the value becomes more accurate.
- Sometimes, iteration doesn’t work, these functions are called divergent, and you must rearrange the formula for x in another way.
- For a successful iterative function, you need a convergent sequence.