PRECISE NUMERICAL RESOLUTION IN TIME OF PARTIAL DERIVATIVE EQUATIONS

Operation co-funded by EU cohesion policy (European Regional Development Fund (ERDF)) under the programme Multi-regional Spain - ERDF (2014ES16RFOP002), managing authority: Subdirección General de Gestión del FEDER, de la Dirección General de Fondos Europeos del Ministerio de Hacienda.. The source names no beneficiary for this operation. Location: Valladolid Province (NUTS ES418); Spain. Budget: total eligible expenditure EUR 31,460; EU co-financing EUR 15,730 (co-financing rate 50%), as stated by the source. Runs 2019-01-01 to 2021-12-31. Source: Kohesio, EU cohesion policy projects managed by national and regional authorities (not CORDIS); selected because its summary names quantum technology. Summary from Kohesio (English machine translation by the source): IT IS WELL KNOWN THAT MANY NATURE MODELS ARE DESCRIBED THROUGH PARTIAL DIFFERENTIAL EQUATIONS. SOME EXAMPLES ARE THE TIME EVOLUTION OF TEMPERATURE IN DIFFERENT LOCATIONS OF AN OBJECT, THE MOVEMENT OF SEA WAVES OR THE FUNCTION WHICH DETERMINES THE PROBABILITY OF FINDING AN ELECTRON IN SOME POINT OF SPACE AND AT A CERTAIN TIME, AT THE CONTEXT OF QUANTUM MECHANICS. HOWEVER, FINDING THE SOLUTION OF THESE EQUATIONS FOR GIVEN INITIAL CONDITIONS AND CONSIDERING THE PARTICULAR BOUNDARY CONDITIONS OF THE PROBLEM IS A TASK WHICH IS RARELY SOLVABLE FROM AN ANALYTIC POINT OF VIEW. THEREFORE, NUMERICAL TECHNIQUES ARE WELL KNOWN TO BE NECESSARY TO APPROXIMATE THE SEARCHED SOLUTION. THE AIM OF THE PROJECT IS TO PROVIDE STRATEGIES AND METHODS WHICH ALLOW TO FIND ACCURATE APPROXIMATIONS WITH THE LEAST POSSIBLE COMPUTATIONAL COST AND, AT THE SAME TIME, TO PERFORM A RIGOROUS MATHEMATICAL ANALYSIS WHICH GUARANTEES AND EXPLAINS THE GOOD BEHAVIOUR OF THESE METHODS. AS THE SPATIAL DISCRETIZATION OF PARTIAL DIFFERENTIAL EQUATIONS GIVES RISE TO SYSTEMS WHICH ARE DENOTED AS STIFF, AND FOR THEM THE CLASSICAL METHODS OF TIME INTEGRATION MUST BE IMPLICIT IN ORDER TO BE STABLE, A BIG PART OF OUR RESEARCH AIMS WILL BE CENTERED ON EXPONENTIAL TIME INTEGRATION. THE LATTER INTEGRATE THE LINEAR AND STIFF PART OF THE PROBLEM IN AN EXACT WAY AND PROVIDE AN INTEGRATION WHICH IS BOTH EXPLICIT AND STABLE. ONE OF THE MAIN AIMS OF THE PROJECT IS TO DESIGN A TECHNIQUE TO TRY TO AVOID THE ORDER REDUCTION WHICH ARISES WITH THESE METHODS WHEN CONSIDERING NON-PERIODIC OR NOT ENOUGH VANISHING BOUNDARY CONDITIONS. WE HAVE ALREADY DESIGNED SEVERAL TECHNIQUES AND PERFORMED AN EXHAUSTIVE ANALYSIS WITH SEVERAL EXPONENTIAL METHODS WHEN THE PROBLEMS ARE NONLINEAR. HOWEVER, THE NONLINEAR HAS NOT YET BEEN DEALT WITH, EITHER FOR REACTION-DIFFUSION PROBLEMS, OF FIRST-ORDER IN TIME, NEITHER FOR SECOND-ORDER IN TIME PROBLEMS. WITH THIS PROJECT, WE WILL CENTER ON EXPONENTIAL RUNGE-KUTTA, SPLITTING-TYPE AND [shortened; the full text is on the Kohesio page]

Original source.

Source: Kohesio (EU cohesion policy projects), European Commission, Directorate-General for Regional and Urban Policy (DG REGIO). Retrieved 2026-10-21. Licence: CC0 1.0 (Cohesion Open Data Platform, dataset 2014-2020 Kohesio projects). Selected metadata, adapted presentation; the publisher's record is authoritative. No endorsement by the source is implied. Licence: public domain dedication (CC0 1.0).

AI-assisted summary: The operation titled "PRECISE NUMERICAL RESOLUTION IN TIME OF PARTIAL DERIVATIVE EQUATIONS" is co-funded by the EU under the Multi-regional Spain programme, with a budget of EUR 31,460. It runs from January 1, 2019, to December 31, 2021, in Valladolid Province, Spain. Suggested technology pillar: simulation. Generated by AI from the public source text; it may contain errors and the original source is authoritative.