mathjs/docs/reference/functions/solveODE.md

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Function solveODE #

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]

Syntax #

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

Parameters #

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

Returns #

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

Throws #

Type	Description

Examples #

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 })

See also #

derivative, simplifyCore