Matlab-compatible ODE solvers in core-Octave Further details are available in this book. The project will complete the implementation of the bvp4c solver that is already available in an initial version in the odepkg packageīy adding a proper error estimator and will implement a matlab-compatible version of the bvp5c solver.ĭetails on the methods to be implemented can be found in this paper on bvp4c and this paper on bvp5c. Implement solver for 1D nonlinear boundary value problems In addition, this page provides some useful material. A good starting point is the method of lines for which you can find more details here and here, whereas an example implementation can be found here. The project will deliver a solver for initial-boundary value problems for parabolic-elliptic PDEs in 1D similar to Matlab's function pdepe. Implement solver for initial-boundary value problems for parabolic-elliptic PDEs in 1D (This is now partly implemented in the lssa package.) Evaluate harmonics and cross-correlations of unevenly sampled and nonstationary time series, as in (which has C code with interface to R).Make QR more memory efficient for large matrices when not all the columns of Q are required (apparently this is not handled by the lapack code yet).Move rand, eye, xpow, xdiv, etc., functions to the matrix classes.Add optional arguments to colloc so that it's not restricted to Legendre polynomials.Make it easy to extend it to other polynomial types. Fix CollocWt? to handle Laguerre polynomials.

Make functions like gamma() return the right IEEE Inf or NaN values for extreme args or other undefined cases.

Iserles and Powell, Clarendon Press, Oxford, 1987) for explicit trigonometric formulae. Kahan, ``Branch Cuts for Complex Elementary Functions, or Much Ado About Nothing's Sign Bit (in The State of the Art in Numerical Analysis, eds. The existing implementation uses a 2005 paper.

Review implementing algorithm in this 2009 paper ( ) for xsum (sum with extra accuracy).

Use pairwise addition in sum() to mitigate against numerical errors without substantial performance penalty ( ).

Improve logm, and sqrtm (see this thread: ).

Implement RandStream objects as Matlab does. Write link between Octave functions (rand, randi, randn, rande) and C++ API.

Use C++11 libraries for random number generation.

Create a graphical design tool for tuning closed loop control system (Control package) 2.1 GUI Variable Editor and Property Inspector.1.6 Improve iterative methods for sparse linear systems.1.4 High Precision Arithmetic Computation.1.3 Matlab-compatible ODE solvers in core-Octave.1.2 Implement solver for 1D nonlinear boundary value problems.1.1 Implement solver for initial-boundary value problems for parabolic-elliptic PDEs in 1D.

Random number generator gnu octave