THE PROPOSED RESEARCH SEEKS TO DEFINE THE MOST PROMISING APPROACHES LEADING TO THE DEVELOPMENT OF AN EXPERT SYSTEM FOR THE SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS.

THE PROPOSED RESEARCH SEEKS TO DEFINE THE MOST PROMISING APPROACHES LEADING TO THE DEVELOPMENT OF AN EXPERT SYSTEM FOR THE SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS. PHASE I WILL ESTABLISH THE TAXONOMY OF PDE'S WHICH WILL BE INCORPORATED IN THE SOLVER'S KNOWLEDGE BASE, AND WILL STUDY AND DEFINE THE COMPOSITION OF THE RULE BASE. THE OBJECTIVE OF THE RESEARCH IS TO PROVIDE APPROACHES TO AUTOMATIC SOLUTION METHOD SELECTION AND AUTOMATIC CODE GENERATION FOR RESEARCHERS WHO HAVE NEITHER THE TIME AND/OR THE KNOWLEDGE TO EFFECTIVELY SOLVE THE PDE OF INTEREST TO THEM. IN ADDITION, THE SYSTEM SHOULD ASSIST THE RESEARCHER IN OBTAINING A CORRECT SOLUTION, BY DETERMINING IF THE PROBLEM IS WELL POSED IN THE DOMAIN OF INTEREST. OTHER AIDS TO THE USER WHICH CAN PROVIDE ADDITIONAL INSIGHT INTO THE EQUATION BEING SOLVED, SUCH AS AUTOMATIC SYMBOLIC TRANSFORMATION OF THE PROBLEM TO NEW COORDINATE SYSTEMS, WILL ALSO BE STUDIED.REVIEW OF PREVIOUS WORK IN THIS AREA WILL BE CONDUCTED, AND AN ASSESSMENT OF THE PROSPECTS FOR CREATING THIS TYPE OF SOFTWARE WILL BE MADE. PHASE II WILL SEEK THE IMPLEMENTATION OF A PROTOTYPE SYSTEM,WHILE PHASE III WILL MAKE THE SYSTEMS AVAILABLE TO THE RESEARCH COMMUNITY.