Beatrice PATERNOSTER | SCIENTIFIC COMPUTING

cod. 0522200045

SCIENTIFIC COMPUTING

	0522200045
	DIPARTIMENTO DI MATEMATICA
	EQF7
	MATHEMATICS
	2020/2021

CURRICULUM APPLICATION-ORIENTED MATHEMATICS

	OBBLIGATORIO
	YEAR OF COURSE 1
	YEAR OF DIDACTIC SYSTEM 2018
	PRIMO SEMESTRE

TEACHING UNITS

	SSD	CFU	HOURS	ACTIVITY	TYPE OF ACTIVITY
	MAT/08	6	48	LESSONS	COMPULSORY SUBJECTS, CHARACTERISTIC OF THE CLASS

PROFESSORS

	BEATRICE PATERNOSTER T Curriculum
	DAJANA CONTE Curriculum

	Objectives
	KNOWLEDGE AND UNDERSTANDING: THE AIM OF THE COURSE IS THE THEORETICAL KNOWLEDGE AND CRITICAL ANALYSIS OF THE MAIN NUMERICAL METHODS FOR THE SOLUTION OF PROBLEMS MODELED BY ORDINARY DIFFERENTIAL EQUATIONS, TOGETHER WITH THE DEVELOPMENT OF THE CORRESPONDING MATHEMATICAL SOFTWARE. PART OF THE COURSE WILL DEAL WITH THE STUDY OF ELEMENTS OF PARALLEL CALCULUS FOR LINEAR ALGEBRA. THE AIM OF THE COURSE IS TO MAKE THE STUDENT CAPABLE TO •SOLVE SYSTEMS OF ORDINARY DIFFERENTIAL EQUATIONS (ALSO LARGE SYSTEMS) BY USING MATHEMATICAL SOFTWARE •THEORETICALLY AND EXPERIMENTALLY ANALYZE THE PROPERTIES OF NUMERICAL METHODS FOR ODES: CONVERGENCE, STABILITY, SIMPLECTICITY •CHOOSE THE MORE APPROPRIATE NUMERICAL METHOD TO SOLVE THE PROBLEM UNDER EXAMINATION

KNOWLEDGE AND UNDERSTANDING:
THE AIM OF THE COURSE IS THE THEORETICAL KNOWLEDGE AND CRITICAL ANALYSIS OF THE MAIN NUMERICAL METHODS FOR THE SOLUTION OF PROBLEMS MODELED BY ORDINARY DIFFERENTIAL EQUATIONS, TOGETHER WITH THE DEVELOPMENT OF THE CORRESPONDING MATHEMATICAL SOFTWARE.
PART OF THE COURSE WILL DEAL WITH THE STUDY OF ELEMENTS OF PARALLEL CALCULUS FOR LINEAR ALGEBRA.

THE AIM OF THE COURSE IS TO MAKE THE STUDENT CAPABLE TO
•SOLVE SYSTEMS OF ORDINARY DIFFERENTIAL EQUATIONS (ALSO LARGE SYSTEMS) BY USING MATHEMATICAL SOFTWARE
•THEORETICALLY AND EXPERIMENTALLY ANALYZE THE PROPERTIES OF NUMERICAL METHODS FOR ODES: CONVERGENCE, STABILITY, SIMPLECTICITY
•CHOOSE THE MORE APPROPRIATE NUMERICAL METHOD TO SOLVE THE PROBLEM UNDER EXAMINATION

	Prerequisites
	THEORY OF ORDINARY DIFFERENTIAL EQUATIONS. BASICS ON PROGRAMMING LANGUAGES MATLAB AND C.

	Contents
	DIFFERENCE EQUATIONS. NUMERICAL METHODS FOR ORDINARY DIFFERENTIAL EQUATIONS: ANALYTICAL APPROXIMATION METHODS, LNEAR MULTISTEP METHODS, PREDICTOR CORRECTOR METHODS, BDF METHODS, RUNGE-KUTTA METHODS, ERROR ESTIMATIONS, CONSISTENCY, CONVERGENCE, ZERO-STABILITY. THEORY OF WEAK STABILITY. STIFF SYSTEMS. STRUCTURE OF A VARIABLE STEPSIZE ALGORITHM. STARTING PROCEDURES. LOCAL TRUNCATION ERROR ESTIMATION. STRATEGIES FOR STEPSIZE CHANGING. MATHEMATICAL SOFTWARE EVALUATION.

Contents

DIFFERENCE EQUATIONS. NUMERICAL METHODS FOR ORDINARY DIFFERENTIAL EQUATIONS: ANALYTICAL APPROXIMATION METHODS, LNEAR MULTISTEP METHODS, PREDICTOR CORRECTOR METHODS, BDF METHODS, RUNGE-KUTTA METHODS, ERROR ESTIMATIONS, CONSISTENCY, CONVERGENCE, ZERO-STABILITY. THEORY OF WEAK STABILITY. STIFF SYSTEMS. STRUCTURE OF A VARIABLE STEPSIZE ALGORITHM. STARTING PROCEDURES. LOCAL TRUNCATION ERROR ESTIMATION. STRATEGIES FOR STEPSIZE CHANGING. MATHEMATICAL SOFTWARE EVALUATION.

	Teaching Methods
	THE TEACHING IS COMPOSED OF FRONTAL LESSONS AND EXERCISES. THE FRONTAL LESSONS WILL PRESENT THE METHODOLOGIES AND THE ALGORITHMS THAT THEN, DURING THE EXERCISES, WILL BE CODED IN SCIENTIFIC CALCULATION ENVIRONMENTS AND TESTED ON TEST PROBLEMS OF INTEREST. PART OF THE EXERCISES WILL BE DEDICATED TO PROJECT ACTIVITIES IN SMALL GROUPS, FOR THE PURPOSE OF DEVELOPING MATHEMATICAL SOFTWARE AND TESTING IT ON TEST PROBLEMS PROVIDED BY THE TEACHER, VERIFYING THE PROPERTIES OF ACCURACY, STABILITY AND EFFICIENCY OF THE METHODS. WORKING IN SMALL GROUPS ALSO AIMS TO GET STUDENTS USED TO GROUP WORK.

Teaching Methods

THE TEACHING IS COMPOSED OF FRONTAL LESSONS AND EXERCISES.

THE FRONTAL LESSONS WILL PRESENT THE METHODOLOGIES AND THE ALGORITHMS THAT THEN, DURING THE EXERCISES, WILL BE CODED IN SCIENTIFIC CALCULATION ENVIRONMENTS AND TESTED ON TEST PROBLEMS OF INTEREST.

PART OF THE EXERCISES WILL BE DEDICATED TO PROJECT ACTIVITIES IN SMALL GROUPS, FOR THE PURPOSE OF DEVELOPING MATHEMATICAL SOFTWARE AND TESTING IT ON TEST PROBLEMS PROVIDED BY THE TEACHER, VERIFYING THE PROPERTIES OF ACCURACY, STABILITY AND EFFICIENCY OF THE METHODS. WORKING IN SMALL GROUPS ALSO AIMS TO GET STUDENTS USED TO GROUP WORK.

	Verification of learning
	THE FINAL EXAM CONSISTS IN THE DISCUSSION OF A PRACTICAL PART IN THE LABORATORY AND AN ORAL PART ON THE CONTENTS OF THE COURSE. THE PRACTICAL PARTY REGARDS THE USE OF THE MATHEMATICAL SOFTWARE DEVELOPED DURING THE TEACHING, TO BE APPLIED TO CERTAIN TEST PROBLEMS BASED ON ORDINARY DIFFERENTIAL EQUATIONS, TO CHECK THE ABILITY TO APPLY THE ACQUIRED KNOWLEDGE. THE ORAL PART REGARDS THE THEORETICAL CONTENTS OF TEACHING, IN ORDER TO CHECK THE ABILITY TO ANALYZING AND PRESENTING WITH RIGOR THE PROPERTIES OF NUMERICAL METHODS FOR ORDINARY DIFFERENTIAL EQUATIONS PRESENTED DURING THE LESSONS.

Verification of learning

THE FINAL EXAM CONSISTS IN THE DISCUSSION OF A PRACTICAL PART IN THE LABORATORY AND AN ORAL PART ON THE CONTENTS OF THE COURSE. THE PRACTICAL PARTY REGARDS THE USE OF THE MATHEMATICAL SOFTWARE DEVELOPED DURING THE TEACHING, TO BE APPLIED TO CERTAIN TEST PROBLEMS BASED ON ORDINARY DIFFERENTIAL EQUATIONS, TO CHECK THE ABILITY TO APPLY THE ACQUIRED KNOWLEDGE. THE ORAL PART REGARDS THE THEORETICAL CONTENTS OF TEACHING, IN ORDER TO CHECK THE ABILITY TO ANALYZING AND PRESENTING WITH RIGOR THE PROPERTIES OF NUMERICAL METHODS FOR ORDINARY DIFFERENTIAL EQUATIONS PRESENTED DURING THE LESSONS.

	Texts
	J.D.LAMBERT, NUMERICAL METHODS FOR ORDINARY DIFFERENTIAL SYSTEMS, J. WILEY & SONS, 1991. HAIRER, LUBICH, WANNER, GEOMETRIC NUMERICAL INTEGRATION, SPRINGER

	More Information
	TEACHERS' E-MAIL: BEAPAT@UNISA.IT, DAJCONTE@UNISA.IT

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Beatrice PATERNOSTER | SCIENTIFIC COMPUTING