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Title: Integration (scipy.integrate) — SciPy v1.18.0.dev Manual

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Domain: scipy.github.io

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docsearch:version1.18.0.dev
docbuild:last-updateFeb 11, 2026

Links:

Skip to main contenthttps://scipy.github.io/devdocs/tutorial/integrate.html#main-content
SciPy https://scipy.github.io/devdocs/index.html
Installing https://scipy.org/install/
User Guide https://scipy.github.io/devdocs/tutorial/index.html
API reference https://scipy.github.io/devdocs/reference/index.html
Building from source https://scipy.github.io/devdocs/building/index.html
Development https://scipy.github.io/devdocs/dev/index.html
Release notes https://scipy.github.io/devdocs/release.html
GitHubhttps://github.com/scipy/scipy
Scientific Python Forumhttps://discuss.scientific-python.org/c/contributor/scipy/
Installing https://scipy.org/install/
User Guide https://scipy.github.io/devdocs/tutorial/index.html
API reference https://scipy.github.io/devdocs/reference/index.html
Building from source https://scipy.github.io/devdocs/building/index.html
Development https://scipy.github.io/devdocs/dev/index.html
Release notes https://scipy.github.io/devdocs/release.html
GitHubhttps://github.com/scipy/scipy
Scientific Python Forumhttps://discuss.scientific-python.org/c/contributor/scipy/
Fourier Transforms (scipy.fft)https://scipy.github.io/devdocs/tutorial/fft.html
Integration (scipy.integrate)https://scipy.github.io/devdocs/tutorial/integrate.html
Interpolation (scipy.interpolate)https://scipy.github.io/devdocs/tutorial/interpolate.html
File IO (scipy.io)https://scipy.github.io/devdocs/tutorial/io.html
Linear Algebra (scipy.linalg)https://scipy.github.io/devdocs/tutorial/linalg.html
Multidimensional Image Processing (scipy.ndimage)https://scipy.github.io/devdocs/tutorial/ndimage.html
Optimization (scipy.optimize)https://scipy.github.io/devdocs/tutorial/optimize.html
Signal Processing (scipy.signal)https://scipy.github.io/devdocs/tutorial/signal.html
Sparse Arrays (scipy.sparse)https://scipy.github.io/devdocs/tutorial/sparse.html
Spatial Data Structures and Algorithms (scipy.spatial)https://scipy.github.io/devdocs/tutorial/spatial.html
Special Functions (scipy.special)https://scipy.github.io/devdocs/tutorial/special.html
Statistics (scipy.stats)https://scipy.github.io/devdocs/tutorial/stats.html
Sparse eigenvalue problems with ARPACKhttps://scipy.github.io/devdocs/tutorial/arpack.html
Compressed Sparse Graph Routines (scipy.sparse.csgraph)https://scipy.github.io/devdocs/tutorial/csgraph.html
Parallel execution support in SciPyhttps://scipy.github.io/devdocs/tutorial/parallel_execution.html
Thread Safety in SciPyhttps://scipy.github.io/devdocs/tutorial/thread_safety.html
https://scipy.github.io/devdocs/index.html
SciPy User Guidehttps://scipy.github.io/devdocs/tutorial/index.html
scipy.integratehttps://scipy.github.io/devdocs/reference/integrate.html#module-scipy.integrate
#https://scipy.github.io/devdocs/tutorial/integrate.html#integration-scipy-integrate
scipy.integratehttps://scipy.github.io/devdocs/reference/integrate.html#module-scipy.integrate
quadhttps://scipy.github.io/devdocs/reference/generated/scipy.integrate.quad.html#scipy.integrate.quad
#https://scipy.github.io/devdocs/tutorial/integrate.html#general-integration-quad
quadhttps://scipy.github.io/devdocs/reference/generated/scipy.integrate.quad.html#scipy.integrate.quad
quadhttps://scipy.github.io/devdocs/reference/generated/scipy.integrate.quad.html#scipy.integrate.quad
quadhttps://scipy.github.io/devdocs/reference/generated/scipy.integrate.quad.html#scipy.integrate.quad
special.expnhttps://scipy.github.io/devdocs/reference/generated/scipy.special.expn.html#scipy.special.expn
quadhttps://scipy.github.io/devdocs/reference/generated/scipy.integrate.quad.html#scipy.integrate.quad
quadhttps://scipy.github.io/devdocs/reference/generated/scipy.integrate.quad.html#scipy.integrate.quad
quadhttps://scipy.github.io/devdocs/reference/generated/scipy.integrate.quad.html#scipy.integrate.quad
quadhttps://scipy.github.io/devdocs/reference/generated/scipy.integrate.quad.html#scipy.integrate.quad
dblquadhttps://scipy.github.io/devdocs/reference/generated/scipy.integrate.dblquad.html#scipy.integrate.dblquad
tplquadhttps://scipy.github.io/devdocs/reference/generated/scipy.integrate.tplquad.html#scipy.integrate.tplquad
nquadhttps://scipy.github.io/devdocs/reference/generated/scipy.integrate.nquad.html#scipy.integrate.nquad
#https://scipy.github.io/devdocs/tutorial/integrate.html#general-multiple-integration-dblquad-tplquad-nquad
dblquadhttps://scipy.github.io/devdocs/reference/generated/scipy.integrate.dblquad.html#scipy.integrate.dblquad
tplquadhttps://scipy.github.io/devdocs/reference/generated/scipy.integrate.tplquad.html#scipy.integrate.tplquad
nquadhttps://scipy.github.io/devdocs/reference/generated/scipy.integrate.nquad.html#scipy.integrate.nquad
#https://scipy.github.io/devdocs/tutorial/integrate.html#gaussian-quadrature
fixed_quadhttps://scipy.github.io/devdocs/reference/generated/scipy.integrate.fixed_quad.html#scipy.integrate.fixed_quad
special.legendrehttps://scipy.github.io/devdocs/reference/generated/scipy.special.legendre.html#scipy.special.legendre
#https://scipy.github.io/devdocs/tutorial/integrate.html#integrating-using-samples
rombhttps://scipy.github.io/devdocs/reference/generated/scipy.integrate.romb.html#scipy.integrate.romb
trapezoidhttps://scipy.github.io/devdocs/reference/generated/scipy.integrate.trapezoid.html#scipy.integrate.trapezoid
simpsonhttps://scipy.github.io/devdocs/reference/generated/scipy.integrate.simpson.html#scipy.integrate.simpson
#https://scipy.github.io/devdocs/tutorial/integrate.html#faster-integration-using-low-level-callback-functions
scipy.LowLevelCallablehttps://scipy.github.io/devdocs/reference/generated/scipy.LowLevelCallable.html#scipy.LowLevelCallable
quadhttps://scipy.github.io/devdocs/reference/generated/scipy.integrate.quad.html#scipy.integrate.quad
dblquadhttps://scipy.github.io/devdocs/reference/generated/scipy.integrate.dblquad.html#scipy.integrate.dblquad
tplquadhttps://scipy.github.io/devdocs/reference/generated/scipy.integrate.tplquad.html#scipy.integrate.tplquad
nquadhttps://scipy.github.io/devdocs/reference/generated/scipy.integrate.nquad.html#scipy.integrate.nquad
quadhttps://scipy.github.io/devdocs/reference/generated/scipy.integrate.quad.html#scipy.integrate.quad
ctypeshttps://docs.python.org/3/library/ctypes.html#module-ctypes
ctypeshttps://docs.python.org/3/library/ctypes.html#module-ctypes
ctypeshttps://docs.python.org/3/library/ctypes.html#module-ctypes
nquadhttps://scipy.github.io/devdocs/reference/generated/scipy.integrate.nquad.html#scipy.integrate.nquad
solve_ivphttps://scipy.github.io/devdocs/reference/generated/scipy.integrate.solve_ivp.html#scipy.integrate.solve_ivp
#https://scipy.github.io/devdocs/tutorial/integrate.html#ordinary-differential-equations-solve-ivp
solve_ivphttps://scipy.github.io/devdocs/reference/generated/scipy.integrate.solve_ivp.html#scipy.integrate.solve_ivp
special.airyhttps://scipy.github.io/devdocs/reference/generated/scipy.special.airy.html#scipy.special.airy
solve_ivphttps://scipy.github.io/devdocs/reference/generated/scipy.integrate.solve_ivp.html#scipy.integrate.solve_ivp
solve_ivphttps://scipy.github.io/devdocs/reference/generated/scipy.integrate.solve_ivp.html#scipy.integrate.solve_ivp
solve_ivphttps://scipy.github.io/devdocs/reference/generated/scipy.integrate.solve_ivp.html#scipy.integrate.solve_ivp
solve_ivphttps://scipy.github.io/devdocs/reference/generated/scipy.integrate.solve_ivp.html#scipy.integrate.solve_ivp
solve_ivphttps://scipy.github.io/devdocs/reference/generated/scipy.integrate.solve_ivp.html#scipy.integrate.solve_ivp
solve_ivphttps://scipy.github.io/devdocs/reference/generated/scipy.integrate.solve_ivp.html#scipy.integrate.solve_ivp
solve_ivphttps://scipy.github.io/devdocs/reference/generated/scipy.integrate.solve_ivp.html#scipy.integrate.solve_ivp
solve_ivphttps://scipy.github.io/devdocs/reference/generated/scipy.integrate.solve_ivp.html#scipy.integrate.solve_ivp
solve_ivphttps://scipy.github.io/devdocs/reference/generated/scipy.integrate.solve_ivp.html#scipy.integrate.solve_ivp
RK45https://scipy.github.io/devdocs/reference/generated/scipy.integrate.RK45.html#scipy.integrate.RK45
Radauhttps://scipy.github.io/devdocs/reference/generated/scipy.integrate.Radau.html#scipy.integrate.Radau
#https://scipy.github.io/devdocs/tutorial/integrate.html#solving-a-system-with-a-banded-jacobian-matrix
odeinthttps://scipy.github.io/devdocs/reference/generated/scipy.integrate.odeint.html#scipy.integrate.odeint
[MOL]https://scipy.github.io/devdocs/tutorial/integrate.html#mol
http://groups.csail.mit.edu/mac/projects/amorphous/GrayScott/http://groups.csail.mit.edu/mac/projects/amorphous/GrayScott/
#https://scipy.github.io/devdocs/tutorial/integrate.html#equation-interior
#https://scipy.github.io/devdocs/tutorial/integrate.html#equation-boundary0
#https://scipy.github.io/devdocs/tutorial/integrate.html#equation-boundaryl
(1)https://scipy.github.io/devdocs/tutorial/integrate.html#equation-interior
(2)https://scipy.github.io/devdocs/tutorial/integrate.html#equation-boundary0
(3)https://scipy.github.io/devdocs/tutorial/integrate.html#equation-boundaryl
odeinthttps://scipy.github.io/devdocs/reference/generated/scipy.integrate.odeint.html#scipy.integrate.odeint
odeinthttps://scipy.github.io/devdocs/reference/generated/scipy.integrate.odeint.html#scipy.integrate.odeint
odeinthttps://scipy.github.io/devdocs/reference/generated/scipy.integrate.odeint.html#scipy.integrate.odeint
odeinthttps://scipy.github.io/devdocs/reference/generated/scipy.integrate.odeint.html#scipy.integrate.odeint
#https://scipy.github.io/devdocs/tutorial/integrate.html#references
MOLhttps://scipy.github.io/devdocs/tutorial/integrate.html#id1
https://en.wikipedia.org/wiki/Method_of_lineshttps://en.wikipedia.org/wiki/Method_of_lines
previous Fourier Transforms (scipy.fft) https://scipy.github.io/devdocs/tutorial/fft.html
next Interpolation (scipy.interpolate) https://scipy.github.io/devdocs/tutorial/interpolate.html
General integration (quad)https://scipy.github.io/devdocs/tutorial/integrate.html#general-integration-quad
General multiple integration (dblquad, tplquad, nquad)https://scipy.github.io/devdocs/tutorial/integrate.html#general-multiple-integration-dblquad-tplquad-nquad
Gaussian quadraturehttps://scipy.github.io/devdocs/tutorial/integrate.html#gaussian-quadrature
Integrating using Sampleshttps://scipy.github.io/devdocs/tutorial/integrate.html#integrating-using-samples
Faster integration using low-level callback functionshttps://scipy.github.io/devdocs/tutorial/integrate.html#faster-integration-using-low-level-callback-functions
Ordinary differential equations (solve_ivp)https://scipy.github.io/devdocs/tutorial/integrate.html#ordinary-differential-equations-solve-ivp
Solving a system with a banded Jacobian matrixhttps://scipy.github.io/devdocs/tutorial/integrate.html#solving-a-system-with-a-banded-jacobian-matrix
Referenceshttps://scipy.github.io/devdocs/tutorial/integrate.html#references
Sphinxhttps://www.sphinx-doc.org/
PyData Sphinx Themehttps://pydata-sphinx-theme.readthedocs.io/en/stable/index.html

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