NUMERICAL METHODS FOR SOLVING BOUNDARY VALUE PROBLEMS OF THE WAVE EQUATION
Annu Kumari,Research Scholar,
Dr. Vineeta Basotia ,Research Guide
Department of Mathematics, Shri JJT University, Jhunjhunu, Rajasthan, India
Abstract : This study examines the dual dimensions of migration-led urbanization in the Shekhawati region, highlighting how migration acts both as a catalyst for development and a source of urban stress. Understanding these challenges and opportunities is essential for formulating sustainable urban policies that balance economic growth, heritage conservation, and environmental resilience in the region. Migration-led urbanization has emerged as a significant driver of socio-economic and spatial transformation in the Shekhawati region of Rajasthan. Traditionally characterized by semi-arid conditions, agrarian livelihoods, and heritage towns, the region is increasingly influenced by rural-to-urban and inter-regional migration in search of employment, education, and improved living standards. This process has created new opportunities such as economic diversification, growth of service sectors, enhanced connectivity, and cultural exchange. At the same time, it has generated several challenges, including unplanned urban expansion, pressure on housing and infrastructure, water scarcity, environmental degradation, and the erosion of traditional socio-cultural structures. Smaller towns in Shekhawati often lack adequate governance capacity and planning mechanisms to manage the growing migrant population, leading to informal settlements and uneven access to basic services.
Keywords: Wave equation, Boundary value problems, Numerical methods, Finite difference method, Finite element method, Spectral methods, Stability analysis
