ode45 — Solve nonstiff ODE systems using adaptive Dormand-Prince 5(4) integration.
ode45 integrates nonstiff first-order ODE systems over tspan using adaptive RK45 stepping and returns MATLAB-compatible time/state outputs.
Syntax
y = ode45(odefun, tspan, y0)
y = ode45(odefun, tspan, y0, options)
[t, y] = ode45(odefun, tspan, y0)
[t, y] = ode45(odefun, tspan, y0, options)Inputs
| Name | Type | Required | Default | Description |
|---|---|---|---|---|
odefun | Any | Yes | — | ODE right-hand-side callback f(t,y). |
tspan | Any | Yes | — | Time interval or monotonic time vector. |
y0 | Any | Yes | — | Initial state vector/value. |
options | Any | No | — | Optional struct with tolerances and step controls. |
Returns
| Name | Type | Description |
|---|---|---|
y | NumericArray | Solution states evaluated over tspan. |
t | NumericArray | Time points selected by solver. |
y | NumericArray | Solution states at each returned time point. |
Returned values from ode45 depend on how many outputs the caller requests.
Errors
| Identifier | When | Message |
|---|---|---|
RunMat:ode45:InvalidArgument | Input argument count/options struct grammar is invalid. | ode45: invalid argument |
RunMat:ode45:InvalidInput | ODE input/state/callback semantics are invalid for integration. | ode45: invalid input |
RunMat:ode45:Internal | Internal output materialization fails. | ode45: internal runtime failure |
How ode45 works
- Supports scalar, vector, and matrix-valued initial conditions.
- Accepts options as a struct, including
RelTol,AbsTol,InitialStep, andMaxStep. - The documented tspan, y0, and derivative domains are single or double. Native integer and logical solver values are independently gated RunMat extensions, and every integer-to-double solver boundary requires exact representability.
- Typed integer
MaxStepsis parsed as an exact structural count; integer floating controls are checked before conversion. - The current RunMat integration loop and outputs are double even when all floating inputs are single; native-single output propagation remains a general compatibility gap rather than an integer extension.
- Event outputs and solution-structure forms are not implemented by the current core solver surface.
- When
tspanhas more than two points, the solver returns values at each requested time. - With one output, returns only the
ytrajectory matrix.
Example
Integrate exponential decay
[t, y] = ode45(@(t, y) -y, [0 5], 1)Expected output:
y(end) ≈ exp(-5)Using ode45 with coding agents
Open a RunMat example with live inputs, then ask the agent to explain how ode45 changes the result.
Run a small ode45 example, explain the result, then change one input and compare the output.
Related Math functions
Elementwise
abs · angle · bsxfun · complex · conj · double · erf · erfcinv · exp · expm1 · factorial · flintmax · gamma · gammaln · heaviside · hypot · idivide · imag · intmax · intmin · ldivide · log · log10 · log1p · log2 · minus · nextpow2 · plus · pow2 · power · rdivide · real · realmax · realmin · realsqrt · rescale · sign · single · sqrt · swapbytes · times · typecast · uint16 · uint32 · uint8
Trigonometry
acos · acosh · asin · asinh · atan · atan2 · atanh · cos · cosd · cosh · cospi · deg2rad · pol2cart · rad2deg · sin · sind · sinh · sinpi · tan · tand · tanh
Reduction
all · any · bounds · cummax · cummin · cumprod · cumsum · cumtrapz · diff · gradient · max · maxk · mean · median · min · mink · movmax · movmean · movmedian · movmin · movprod · movstd · movsum · movvar · nnz · prod · rms · std · sum · trapz · var
Structure
bandwidth · isdiag · ishermitian · issymmetric · istril · istriu · symrcm
Signal
blackman · butter · buttord · cheb2ord · conv · conv2 · deconv · downsample · envelope · filter · filtfilt · fir1 · freqz · gauspuls · hamming · hann · hilbert · periodogram · pulstran · pwelch · rectpuls · resample · sawtooth · sinc · spectrogram · square · tripuls · unwrap · upsample · zplane
Optim
coneprog · fminbnd · fminunc · fsolve · fzero · integral · linprog · lsqcurvefit · lsqnonlin · optimoptions · optimset · quad · secondordercone
Ops
cross · ctranspose · dot · mldivide · mpower · mrdivide · mtimes · pagemtimes · pagetranspose · trace · transpose
Open-source implementation
Unlike proprietary runtimes, every RunMat function is open-source. Read exactly how ode45 is executed, line by line, in Rust.
- View the source for ode45 in Rust on GitHub
- Learn how the RunMat runtime works
- Found a bug? Open an issue with a minimal reproduction.
About RunMat
RunMat is an open-source runtime that executes MATLAB-syntax code blazing on any GPU. It is licensed under the Apache 2.0 license.
- RunMat automatically optimizes your math for GPU execution on Apple, Nvidia, and AMD hardware. No code changes needed. Simulations that took hours now take minutes.
- Start running code in seconds. RunMat runs in the browser, on the desktop, or from the CLI. No license server, no IT ticket.