My Academic Projects (M.Sc.)

Python Package - Solution of ODE

Supervisor : Dr. R.P. Singh and Dr. Harshita Madduri

Developed a Python package for solving first- and second-order ordinary differential equations (ODEs) using numerical methods such as Euler, Modified Euler, Runge-Kutta (RK2, RK4), Taylor Series, Milne’s, and Adams-Bashforth Predictor-Corrector methods. The package supports accurate and efficient solutions for applications in mathematical modeling, engineering, and computational science.

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Codes for Numerical Methods in Python

Supervisor : Prof. ASV Ravi Kanth

We developed a comprehensive Python codes for Numerical Methods, designed to solve various mathematical and engineering problems efficiently. These codes includes implementations of root-finding methods, numerical differentiation and integration, interpolation, linear and non-linear system solvers, and numerical solutions of ODEs and PDEs. It features multiple algorithms such as Newton’s Method, Secant Method, Runge-Kutta Methods The package is optimized for performance and accuracy, making it a valuable tool for students, researchers, and professionals in applied mathematics and computational science.

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Supervisor : Prof. ASV Ravi Kanth

We have developed Python codes using Finite Difference Methods (FDM) to solve ODEs and PDEs efficiently. For parabolic PDEs, we implement FTCS, BTCS, and Crank-Nicholson methods for heat and diffusion problems. For hyperbolic PDEs, we use explicit schemes for wave propagation. For elliptic PDEs, we apply Jacobi, Gauss-Seidel, and SOR methods for steady-state solutions. Using Matplotlib, we visualize results through contour, surface, and time evolution plots, ensuring accuracy and efficiency for researchers and professionals.

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