For more detailed explanations and formulas of each method, refer to the course materials or external resources on numerical methods.

Sinc methods are now recognized as an efficient numerical method for problems whose solutions may have singularities, or infinite domains, or boundary layers. This work deals with the sinc-collocation ...

Some algorithms based upon a projection process onto the Krylov subspace $K_m = \operatorname{Span}(r_0, Ar_0, \ldots, A^{m - 1}r_0)$ are developed, generalizing the ...

The Bi-Section method finds roots of non-linear equations using interval bisection. Initial Range Calculation: Determines an initial maximum range ((-|xmax|, |xmax|)) for root existence. Calculation ...

Pair of Linear Equations in Two Variables Class 10 Notes: Revision notes for CBSE Class 10 Mathematics Chapter 3 Pair of Linear Equations in Two Variables have been presented in the article along with ...

A large number of problems in engineering can be formulated as the optimization of certain functionals. In this paper, we present an algorithm that uses the augmented Lagrangian methods for finding ...

The course provides a thorough introduction to design, analysis (both theoretical and empirical), and programming of popular methods (finite difference and variational methods like finite element) for ...

The analysis of phase decomposition was carried out using the nonlinear and linear Cahn-Hilliard equations in a hypothetical A-B alloy system with a miscibility gap. These equations were solved by the ...