Math

Euler Method ODE Solver

Approximate ODE solutions with the forward Euler method.

Euler Method ODE Solver approximates first-order differential equation solutions over discrete step sizes. It is useful for numerical methods coursework and fast model prototyping. The tool helps visualize how step size affects approximation error. Use it as an introductory solver before more advanced methods.

Euler Method Inputs

Solves dy/dx = a*x + b*y + c.

Result

Final x: 2.00000000

Final y: 3.17466776

n	x	y	dy/dx
0	0.000000	1.000000	0.800000
1	0.100000	1.080000	0.834000
2	0.200000	1.163400	0.867320
3	0.300000	1.250132	0.899974
4	0.400000	1.340129	0.931974
5	0.500000	1.433327	0.963335
6	0.600000	1.529660	0.994068
7	0.700000	1.629067	1.024187
8	0.800000	1.731486	1.053703
9	0.900000	1.836856	1.082629
10	1.000000	1.945119	1.110976
11	1.100000	2.056216	1.138757
12	1.200000	2.170092	1.165982
13	1.300000	2.286690	1.192662
14	1.400000	2.405957	1.218809
15	1.500000	2.527837	1.244433
16	1.600000	2.652281	1.269544
17	1.700000	2.779235	1.294153
18	1.800000	2.908650	1.318270
19	1.900000	3.040477	1.341905
20	2.000000	3.174668	1.365066

How to use this tool

Enter differential equation form, initial value, step size, and interval.
Run Euler iteration to generate approximate solution points.
Compare outputs with smaller step sizes to assess stability.

Numerical methods tools

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