Computational Differential Equations

MA25C09:

Computational Differential Equations

Course Objectives:

• The Objectives of the course are to equip students with the ability to formulate and solve various types of Ordinary and Partial Differential Equations (ODEs & PDEs) and to develop proficiency in applying numerical methods and computational tools for solving differential equations encountered in engineering problems.

First Order Ordinary Differential Equations: Basic concepts of ordinary differential equations–Formation of first order differential equations from physical problems–First order and first-degree ODE: Variables separable–Exact equations–Leibnitz’s equation – Bernoulli’s equation – Numerical Methods: Solving first order ODE by Euler's formula, Taylor series and Runge Kutta method of 4^th order.

Activities: Application and Visualization of the first order ODE using open-source software and solving Competitive Examination questions

Higher Order Ordinary Differential Equations: Formation of second order differential equations from physical problems–Linear equations of second and higher order with constant coefficients – Euler’s linear equations – Method of variation of parameters–Numerical Methods: Solving second order ODE by Runge-Kutta method of 4th order and finite difference method.

Activities: solving ordinary differential equations using open-source software and solving of Competitive Examination questions

First Order Partial Differential Equations: Formation of partial differential equations by elimination of arbitrary constants and arbitrary functions - Solution of PDE by variable separable method – Solution of standard types of first order partial differential equations (excluding reducible to standard types) – Lagrange’s linear equation – Numerical Methods for first order PDE by Method of lines with Runge-Kutta method of order fourth.

Activities: Application and Visualization of the Partial Differential Equations using open-source software and solving Competitive Examination questions

Higher Order Partial Differential Equations: Linear homogeneous partial differential equations of second and higher order with constant coefficients. Numerical Methods: Finite difference techniques for the solution of two-dimensional Laplace’s and Poisson’s equations on rectangular domain—Solution of one-dimensional heat equation using Bender Schmidt and Crank Nicholson difference schemes—Solution of one-dimensional wave equation by explicit scheme.

Activities: Application of the second order PDE using open-source software of 1-D wave, 1-D heat equations, Laplace and Poisson equations and Solving Competitive Examination questions

Weightage: Continuous Assessment: 40%, End Semester Examinations: 60%.

Assessment Methodology: Assignments (20%), Solution to application-oriented problems using software (20%), Solving Competitive Examination questions (20%), Internal Examinations (40%).

References:

1.Erwin Kreyszig, Advanced Engineering Mathematics, (11^th ed.), John Wiley & Sons, USA,2025.

2.Joe D. Hoffman, Numerical Methods for Engineers and Scientists (3^rd ed.). CRC Press (Taylor & Francis Group), 2001.

3.Steven C. Chapra and Raymond P. Canale. Numerical Methods for Engineers

(8th ed.). McGraw-Hill Education, 2021.

4.William E. Boyce and Richard C. DiPrima. Elementary Differential Equations and Boundary Value Problems, (11^thed.). John Wiley & Sons, USA,2017.

5.Grewal B.S., “Higher Engineering Mathematics”, Khanna Publishers, New Delhi, 45^th Edition, 2026.

6.Randall J. LeVeque, Finite Difference Methods for Ordinary and Partial

Differential Equations, SIAM,2007.