Backward Eulers method is a implicit method , also known as modified Euler's method
In Backward Euler method \[Y_{i+1}\]\[=Y_i+hf_{(X_{i+1},Y_{i+1})}\] .............
Example Using Backward Eulers method find the approximate value of y corresponding to x=0.2 given that dy/dx=x+y and y=1 when x=0 use step h=0.1
Solution
| i |
\[X_i\] |
\[X_i\] |
Comments |
| 0 |
0.0 |
1.00 |
intial comments given |
| 1 |
0.1 |
1.122 |
1.122 |
| 2 |
0.2 |
1.2689 |
1.2689 |
So the approximate value of y at x=0.2 is 1.2689
Advantage of Backward Eulers method is its stability .Backward Eulers method is more stable compared to Forward Eulers method.
A method is stable if the effect of any fixed round off error is bounded , independent of the number of mesh points.
