Abstract
Singular boundary-value problems appear frequently on the modellization of many physical phenomena as in catalytic diffusion reactions, chemical kinetics, thermal-explosion theory, or electro hydrodynamics, among others. The singular Lane-Endem equation is a typical kind of equation modelling some of those problems. Unfortunately, just in few occasions the exact solutions can be obtained. In this situation the block methods have been used largely for approximating different kind of differential problems. We propose its use for solving singular boundary value problems. The proposed strategy consist in a block method combined with an appropriate set of formulas which are developed at the first subinterval to circumvent the singularity at the left end of the integration interval. Some examples are presented to validate the efficiency of the proposed strategy.
Highlights
It seems that block methods were firstly proposed by Milne for solving initial-value problems in differential equations
We propose its use for solving singular boundary value problems
The proposed strategy consist in a block method combined with an appropriate set of formulas which are developed at the first subinterval to circumvent the singularity at the left end of the integration interval
Summary
It seems that block methods were firstly proposed by Milne for solving initial-value problems in differential equations (see [1]). A k-step block method is a set of k multistep formulas that produces at the same time k approximate values of the solution of the differential problem at k grid points. This may vary according to the order and the kind of equation considered. If we try to solve this problem with the global method in the previous section we will run into troubles, since the value f0 cannot be obtained To overcome this difficulty we propose to develop a set of multistep formulas to be applied at the first subinterval, [x0, x1], with the purpose of avoid the use of f0. In the numerical examples we have considered mixed boundary conditions
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
