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<h1 id="function-solveode">Function solveODE <a href="#function-solveode" title="Permalink">#</a></h1>

Numerical Integration of Ordinary Differential Equations

Two variable step methods are provided:
- "RK23": Bogacki–Shampine method
- "RK45": Dormand-Prince method RK5(4)7M (default)

The arguments are expected as follows.

- `func` should be the forcing function `f(t, y)`
- `tspan` should be a vector of two numbers or units `[tStart, tEnd]`
- `y0` the initial state values, should be a scalar or a flat array
- `options` should be an object with the following information:
  - `method` ('RK45'): ['RK23', 'RK45']
  - `tol` (1e-3): Numeric tolerance of the method, the solver keeps the error estimates less than this value
  - `firstStep`: Initial step size
  - `minStep`: minimum step size of the method
  - `maxStep`: maximum step size of the method
  - `minDelta` (0.2): minimum ratio of change for the step
  - `maxDelta` (5): maximum ratio of change for the step
  - `maxIter` (1e4): maximum number of iterations

The returned value is an object with `{t, y}` please note that even though `t` means time, it can represent any other independant variable like `x`:
- `t` an array of size `[n]`
- `y` the states array can be in two ways
  - **if `y0` is a scalar:** returns an array-like of size `[n]`
  - **if `y0` is a flat array-like of size [m]:** returns an array like of size `[n, m]`


<h2 id="syntax">Syntax <a href="#syntax" title="Permalink">#</a></h2>

```js
math.solveODE(func, tspan, y0)
math.solveODE(func, tspan, y0, options)
```

<h3 id="parameters">Parameters <a href="#parameters" title="Permalink">#</a></h3>

Parameter | Type | Description
--------- | ---- | -----------
`func` | function | The forcing function f(t,y)
`tspan` | Array &#124; Matrix | The time span
`y0` | number &#124; BigNumber &#124; Unit &#124; Array &#124; Matrix | The initial value
`options` | Object | Optional configuration options

<h3 id="returns">Returns <a href="#returns" title="Permalink">#</a></h3>

Type | Description
---- | -----------
Object | Return an object with t and y values as arrays


<h3 id="throws">Throws <a href="#throws" title="Permalink">#</a></h3>

Type | Description
---- | -----------


<h2 id="examples">Examples <a href="#examples" title="Permalink">#</a></h2>

```js
function func(t, y) {return y}
const tspan = [0, 4]
const y0 = 1
math.solveODE(func, tspan, y0)
math.solveODE(func, tspan, [1, 2])
math.solveODE(func, tspan, y0, { method:"RK23", maxStep:0.1 })
```


<h2 id="see-also">See also <a href="#see-also" title="Permalink">#</a></h2>

[derivative](derivative.html),
[simplifyCore](simplifyCore.html)