Students can plan their studies for board exam preparation with the official CBSE Class 12 Applied Maths syllabus (2026-27).

Abstract: This article presents a new direct solver to solve integral equations arising out of large-scale computational electrostatics. The solver is based on $\mathcal{H}^{2}$ matrices that exploit ...

The nearly analytic discretization of the frequency-domain wave equation produces large-scale, sparse, and ill-conditioned linear system, which challenge conventional iterative solvers. To mitigate ...

Abstract: This paper focuses on the inverse optimal control problem for discrete-time systems with unknown cost functions using linear matrix inequalities (LMIs). Based on Pontryagin's minimum ...

Multi-language suite for high-performance solvers of differential equations and scientific machine learning (SciML) components. Ordinary differential equations (ODEs), stochastic differential ...

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Index laws and the laws of logarithms are essential tools for simplifying and manipulating exponential and logarithmic functions. There is an inverse relationship between exponential and logarithmic ...

Differential equations often give rise to rank-structured matrices characterized by low-rank off-diagonal blocks. These matrices can be conveniently represented in a hierarchical format, enabling ...

8.7 Examples of Solving Stationary Equations 8.7.1 Repair Facility Problem with Cost 8.7.2 Umbrella Problem 8.8 Infinite-State DTMCs 8.9 Infinite-State Stationarity Result 8.10 Solving Stationary ...

The control of general nonlinear systems is a challenging task in particular for large-scale models as they occur in the semi-discretization of partial differential equations (PDEs) of, say, fluid ...