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|stochastic-volterra-integral-equation| image:: https://raw.githubusercontent.com/dsagolla/nssvie/main//docs/source/images/stochastic-volterra-integral-equation.svg\n.. |X-t| image:: https://raw.githubusercontent.com/dsagolla/nssvie/main//docs/source/images/X-t.svg\n.. |f| image:: https://raw.githubusercontent.com/dsagolla/nssvie/main//docs/source/images/f.svg\n.. |k-1-k-2| image:: https://raw.githubusercontent.com/dsagolla/nssvie/main//docs/source/images/k-1-k-2.svg\n.. |B-t| image:: https://raw.githubusercontent.com/dsagolla/nssvie/main//docs/source/images/B-t.svg\n.. |ito-integral| image:: https://raw.githubusercontent.com/dsagolla/nssvie/main//docs/source/images/ito-integral.svg\n.. |example-1-eq| image:: https://raw.githubusercontent.com/dsagolla/nssvie/main//docs/source/images/example-1-eq.svg\n.. |example-1-f| image:: https://raw.githubusercontent.com/dsagolla/nssvie/main/docs/source/images/example-1-f.svg\n.. |example-1-k-1| image:: https://raw.githubusercontent.com/dsagolla/nssvie/main//docs/source/images/example-1-k-1.svg\n.. |example-1-k-2| image:: https://raw.githubusercontent.com/dsagolla/nssvie/main//docs/source/images/example-1-k-2.svg\n\nA python package for computing a numerical solution of stochastic Volterra \nintegral equations of the second kind\n\n|stochastic-volterra-integral-equation|\n\nwhere\n\n+ |X-t| is an unknown process,\n+ |f| is a continuous function,\n+ |k-1-k-2| are continuous and square integrable functions,\n+ |B-t| is the Brownian motion (see `Wiener process \u003chttps://en.wikipedia.org/wiki/Wiener_process\u003e`_) and\n+ |ito-integral| is the Itô-integral (see `Itô calculus \u003chttps://en.wikipedia.org/wiki/It%C3%B4_calculus\u003e`_)\n\nby a stochastic operational matrix based on block\npulse functions as suggested in `Maleknejad et. al (2012) \n\u003chttps://www.sciencedirect.com/science/article/pii/S0895717711005504/\u003e`_ [1]_.\n\n+ `Documentation \u003chttps://nssvie.readthedocs.io/en/latest\u003e`_\n+ `API Reference \u003chttps://nssvie.readthedocs.io/en/latest/api.html\u003e`_\n+ `Source Code \u003chttps://github.com/dsagolla/nssvie\u003e`_\n+ `Bug reports \u003chttps://github.com/dsagolla/nssvie/issues\u003e`_\n\n``nssvie`` is distributed under the terms of the `GNU GPLv3 \u003chttps://www.gnu.org/licenses/gpl-3.0.en.html\u003e`_ license.\n\nInstall\n-------\n\nInstall using either of the following two methods.\n\n1. Install from PyPi\n~~~~~~~~~~~~~~~~~~~~\n\n|pypi| |pyversions| |format| \n\nThe ``nssvie`` package is available on `PyPi \u003chttps://pypi.org/project/nssvie/\u003e`_ and can be installed using ``pip``\n\n.. code-block:: bash\n\n    pip install nssvie\n\n\n2. Install from Source\n~~~~~~~~~~~~~~~~~~~~~~\n\n|release| |licence|\n\nInstall directly from the source code by\n\n.. code-block:: bash\n\n\tgit clone https://github.com/dsagolla/nssvie.git\n\tcd nssvie\n\tpip install .\t\n\nDependencies\n~~~~~~~~~~~~\n\n``nssvie`` uses \n\n+ `NumPy \u003chttps://numpy.org/\u003e`_  for many calculations, \n+ `SciPy \u003chttps://scipy.org\u003e`_ for computing the block pulse coefficients and\n+ `stochastic \u003chttps://pypi.org/project/stochastic/\u003e`_ for sampling the Brownian Motion\n\nUsage \n-----\n\nConsider the following example of a stochastic Volterra integral equation\n\n|example-1-eq|\n\nso \n\n+ |example-1-f| ,   \n+ |example-1-k-1| and   \n+ |example-1-k-2|.\n\n.. code-block:: python\n\n\tfrom nssvie import SVIE\n\timport matplotlib.pyplot as plt\n\t\n\t# Define the function and the kernels of the stochastic Volterra \n\t# integral equation\n\tdef f(t):\n\t\treturn 1.0\n\t\n\tdef k1(s,t):\n\t\treturn s**2\n\t\n\tdef k2(s,t):\n\t\treturn s\n\t\n\t# Generate the stochastic Volterra integral equation\n\tsvie = SVIE(\n\t\tfunction_f=f, kernel_2=k1, kernel_1=k2, endpoint=0.5\n\t)\n\t# Calculate numerical solution with m=20 intervals  \n\tapproximative_solution = svie.solve_numerical(\n\t\tintervals=20\n\t)\n\tfig, ax = plt.subplots()\n\ttimes = [i * 0.5/20 for i in range(21)]\n\tax.step(times, approximative_solution, c='k')\n\tplt.show()\n\n.. image:: https://raw.githubusercontent.com/dsagolla/nssvie/main/docs/source/images/example.png\n\t:align: center\n\nThe parameters are\n\n+ ``function_f``: the function |f|.\n+ ``kernel_1``, ``kernel_2``: the kernels |k-1-k-2|.\n+ ``endpoint``: the right hand side of :math:`[0,T)` (default is ``1.0``),\n+ ``intervals``: the number of intervals to divide :math:`[0,T)` (default is ``50``)\n\nfor the stochastic Volterra integral equation above.\n\nCitation\n--------\n\n.. [1] Maleknejad, K., Khodabin, M., \u0026 Rostami, M. (2012). Numerical solution of stochastic Volterra integral equations by a stochastic operational matrix based on block pulse functions. Mathematical and computer Modelling, 55(3-4), 791-800. |maleknejad-et-al-2012-doi|    \n\n.. |licence| image:: https://img.shields.io/github/license/dsagolla/nssvie\n    :target: https://www.gnu.org/licenses/gpl-3.0.en.html\n.. |pypi| image:: https://img.shields.io/pypi/v/nssvie\n    :target: https://pypi.org/project/nssvie\n.. |release| image:: https://img.shields.io/github/v/release/dsagolla/nssvie?display_name=release\u0026sort=semver\n    :target: https://github.com/dsagolla/nssvie/releases\n.. |format| image:: https://img.shields.io/pypi/format/nssvie\n.. |pyversions| image:: https://img.shields.io/pypi/pyversions/nssvie\n    :target: https://www.python.org/\n.. |maleknejad-et-al-2012-doi| image:: https://img.shields.io/badge/DOI-10.1016%2Fj.mcm.2011.08.053-blue\n    :target: https://doi.org/10.1016/j.mcm.2011.08.053\n    :alt: doi: 10.1016/j.mcm.2011.08.053\n.. |docs| image:: https://readthedocs.org/projects/nssvie/badge/?version=latest\n    :target: https://nssvie.readthedocs.io/en/latest/?badge=latest\n.. |build| image:: https://github.com/dsagolla/nssvie/actions/workflows/build.yml/badge.svg\n\t:target: https://github.com/dsagolla/nssvie/actions/workflows/build.yml\n.. |tests| image:: https://github.com/dsagolla/nssvie/actions/workflows/tests.yml/badge.svg\n\t:target: https://github.com/dsagolla/nssvie/actions/workflows/tests.yml\n.. |linter| image:: https://warehouse-camo.ingress.cmh1.psfhosted.org/d6d741fdb0ae96663fc5e9fbfb16b9ee24d52dfd/68747470733a2f2f696d672e736869656c64732e696f2f62616467652f6c696e74696e672d70796c696e742d79656c6c6f77677265656e\n\t:target: https://github.com/pylint-dev/pylint\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fdsagolla%2Fnssvie","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fdsagolla%2Fnssvie","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fdsagolla%2Fnssvie/lists"}