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ES504 NUM. SOLUTION OF PARTIAL DIFF. EQUATIONS

Course Objectives

By the end of the course, students will be able to:

Understand the classification and properties of PDEs (elliptic, parabolic, hyperbolic).

Formulate initial and boundary-value problems in physical and engineering contexts.

Implement and analyze numerical methods such as finite difference and finite element approaches.

Evaluate the stability, consistency, and convergence of numerical schemes.

Apply numerical techniques to model problems in solid and fluid mechanics.

Develop computational tools to solve practical PDE problems and interpret numerical results.

Course Content

Solution of systems of equations. Initial and boundary-value problems. Parabolic, elliptic and hyperbolic equations. Selected topics from solid and fluid mechanics.

Course Learning Outcomes

Classify partial differential equations (PDEs) and formulate appropriate initial and boundary value problems relevant to engineering applications.
Implement numerical methods for solving PDEs.
Analyze the accuracy, stability, and convergence of numerical schemes for differential equations.
Apply finite difference methods to solve parabolic, elliptic, and hyperbolic PDEs.
Explain the basic principles of the finite element and finite volume methods, and their applicability to different classes of PDEs.
Construct numerical models for problems in solid and fluid mechanics using appropriate discretization methods.
Compare and evaluate the strengths and limitations of different numerical methods for solving PDEs in engineering contexts.
Develop simple computational algorithms or codes to implement numerical methods and interpret simulation results

Program Outcomes Matrix