1. Numerical Methods for ODEs. Compare and contrast two numerical methods (e.g., Euler's method, Runge-Kutta methods) used to solve first-order ODEs. Explain their accuracy and stability in engineering applications; 2. Numerical Techniques for PDEs. Explain the finite difference method and its application in solving partial differential equations. Discuss its suitability and limitations in simulating engineering phenomena; 3. Reservoir Modeling. Explain how numerical methods for solving ODEs are applied in reservoir modeling. Provide specific examples of scenarios in petroleum engineering where ODEs play a crucial role; 4. Accuracy Assessment in Gas Flow Modeling. Evaluate the accuracy of numerical solutions for PDEs when modeling gas flow in reservoirs. Discuss factors that influence the accuracy of simulation results; 5. Challenges in Numerical Simulation for Gas Reservoirs. Discuss specific challenges associated with numerical simulation of gas reservoirs using differential equations. Propose innovative solutions or approaches to address these challenges; 1. Numerical Methods for ODEs. Compare and contrast two numerical methods (e.g., Euler's method, Runge-Kutta methods) used to solve first-order ODEs. Explain their accuracy and stability in engineering applications; 2. Numerical Techniques for PDEs. Explain the finite difference method and its application in solving partial differential equations. Discuss its suitability and limitations in simulating engineering phenomena; 3. Reservoir Modeling. Explain how numerical methods for solving ODEs are applied in reservoir modeling. Provide specific examples of scenarios in petroleum engineering where ODEs play a crucial role; 4. Accuracy Assessment in Gas Flow Modeling. Evaluate the accuracy of numerical solutions for PDEs when modeling gas flow in reservoirs. Discuss factors that influence the accuracy of simulation results; 5. Challenges in Numerical Simulation for Gas Reservoirs. Discuss specific challenges associated with numerical simulation of gas reservoirs using differential equations. Propose innovative solutions or approaches to address these challenges