twpbvpl

Algorithms for the Solution of Two-Point Boundary Value Problems: The Fortran 77 code TWPBVP was originally developed by Jeff Cash and Margaret Wright and is a global method to compute the numerical solution of two point boundary value problems (either linear or non-linear) with separated boundary conditions. In the code TWPBVP, MIRK schemes of orders 4, 6 and 8 are solved in a deferred correction framework in an attempt to give a solution accurate to a prescribed local tolerance at a discrete set of mesh points. TWPBVP has been found to be especially effective at solving non-stiff and mildly-stiff ODEs efficiently. For problems of a greater stiffness, fully implicit Runge Kutta schemes have been found to be more suitable (although requiring more work per step) than MIRK schemes. A deferred correction code TWPBVPL based on Lobatto IIIA schemes of orders 4, 6 and 8 has been developed. For stiff problems it is recommended that this code should be tried first. ...


References in zbMATH (referenced in 11 articles )

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  1. Naceur, Nahed; Khenissi, Moez; Roche, Jean R.: Numerical solution of nonlinear differential boundary value problems using adaptive non-overlapping domain decomposition method (2022)
  2. Ramos, Higinio; Singh, Gurjinder: Solving second order two-point boundary value problems accurately by a third derivative hybrid block integrator (2022)
  3. Amodio, Pierluigi; Giordano, Domenico; Iavernaro, Felice; Labianca, Arcangelo; Lazzo, Monica; Mazzia, Francesca; Pisani, Lorenzo: Mathematical aspects relative to the fluid statics of a self-gravitating perfect-gas isothermal sphere (2020)
  4. Giordano, Domenico; Amodio, Pierluigi; Iavernaro, Felice; Labianca, Arcangelo; Lazzo, Monica; Mazzia, Francesca; Pisani, Lorenzo: Fluid statics of a self-gravitating perfect-gas isothermal sphere (2019)
  5. McLachlan, Robert I.; Offen, Christian: Symplectic integration of boundary value problems (2019)
  6. Temimi, Helmi; Ben-Romdhane, Mohamed; Ansari, Ali R.; Shishkin, Grigorii I.: Finite difference numerical solution of Troesch’s problem on a piecewise uniform Shishkin mesh (2017)
  7. Brdar, Mirjana; Zarin, Helena: On graded meshes for a two-parameter singularly perturbed problem (2016)
  8. Mazzia, Francesca; Nagy, A. M.: A new mesh selection strategy with stiffness detection for explicit Runge-Kutta methods (2015)
  9. Mazzia, Francesca; Cash, Jeff R.; Soetaert, Karline: Solving boundary value problems in the open source software R: package bvpSolve (2014)
  10. Cash, J. R.; Hollevoet, D.; Mazzia, F.; Nagy, A. M.: Algorithm 927: The MATLAB code bvptwp.m for the numerical solution of two point boundary value problems (2013)
  11. Cash, Jeff R.: The numerical solution of nonlinear two-point boundary value problems using iterated deferred correction -- a survey (2006)