A LOCALLY-CONTINUOUS MESHLESS LOCAL PETROV-GALERKIN METHOD APPLIED TO A TWO-POINT BOUNDARY VALUE PROBLEM
IN RECENT YEARS, THE MESHLESS LOCAL PETROV-GALERKIN (MLPG) METHOD HAS ATTRACTED THE ATTENTION OF MANY RESEARCHERS IN SOLVING SEVERAL TYPES OF BOUNDARY VALUE PROBLEMS. THIS METHOD IS BASED ON A LOCAL WEAK FORM, EVALUATED IN LOCAL SUBDOMAINS AND DOES NOT REQUIRE ANY MESH, EITHER IN THE CONSTRUCTION OF THE TEST AND SHAPE FUNCTIONS OR IN THE INTEGRATION PROCESS. HOWEVER, THE SHAPE FUNCTIONS USED IN MLPG HAVE COMPLICATED FORMS, WHICH MAKES THEIR COMPUTATION AND THEIR DERIVATIVE'S COMPUTATION COSTLY. IN THIS WORK, USING THE MOVING LEAST SQUARE (MLS) METHOD, WE DISSOCIATE THE POINT WHERE THE APPROXIMATING POLYNOMIAL'S COEFFICIENTS ARE OPTIMIZED, FROM THE POINTS WHERE ITS DERIVATIVES ARE COMPUTED. WE ARGUE THAT THIS APPROACH NOT ONLY IS CONSISTENT WITH THE UNDERLYING APPROXIMATION HYPOTHESIS, BUT ALSO MAKES COMPUTATION OF DERIVATIVES SIMPLER. WE APPLY OUR APPROACH TO A TWO-POINT BOUNDARY VALUE PROBLEM, AND PERFORM SEVERAL TESTS TO SUPPORT OUR CLAIM. THE RESULTS SHOW THAT THE PROPOSED MODEL IS EFFICIENT, ACHIEVES GOOD PRECISION, AND IS ATTRACTIVE TO BE APPLIED TO OTHER HIGHER-DIMENSION PROBLEMS.
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License [CC BY] that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).