Jugni, Dhola and Mahiya: Comparing

Among the amazing variety of forms of poetic expression by the folk of the Punjab region, this essay has selected three genres: mahiya, dhola and jugni. The study is meant to compare these three genres of Punjabi folklore, in their evolution, structure, expression and themes. The study finds that the three genres are very old in time origin and tracing their exact origins in history is impossible, only few hints are available. Their structures are variable, as mahiya has a fixed structure, dhola has rather loose structure giving more freedom to the singer-poet, and jugni has a specific meter in certain lines, but it has freedom to repeat some lines for perfect expression of the melody. The structures in fact follow the tunes, distinct for each genre. Three genres have many themes common, but jugni has spirituality as dominant theme, dhola has expression of love as dominant them and mahiya has now become quite inclusive, but it originated as expression of love and it still retains that character in its core. The folk heart of Punjab has endeared these three genres so much that these are appreciated far and wide in original tunes, but new experiments of tunes and themes are also underway. Being a true mirror of simple unsophisticated villagers these folk songs would lose popularity if these villagers become sophisticated hence the need for their preservation is highlighted in this study.

Mesh Free Collocation Method for Numerical Solution of Initial-Boundary-Value Problems Using Radial Basis Functions

Nonlinear partial differential equations are often used to understand and model nonlinear processes arising in many branches of science and engineering. For most of partial differential equations a general closed-form analytical solution is not available and therefore use of numerical methods always remains an important alternative for the solution of partial differential equations. Several numerical methods are developed for the solution of partial differential equations including finite difference methods, finite element methods, spectral methods and spline methods. However numerical methods posses some limitations such as mesh generation, slow rate of convergence, spatial dependence, stability, low accuracy and difficult to implement in complex geometries. One of domain type methods is known as radial basis functions method, which is a truly meshless method, infinitely differentiable, numerically accurate, stable, very high rate of convergence, spatial independence and flexible with respect to complex geometry. The main difference between the mesh free radial basis functions method and classical mesh-based methods is that the radial basis functions can be extended to the entire domain of influence without diving into elements. In this thesis, we present mesh free radial basis functions method based on collocation principle for numerical solution of various time dependent nonlinear partial differential equations namely, Regularized Long Wave (RLW) equation, Modified Regularized Long Wave (MRLW) equation, Modified Equal Width Wave (MEW) equation, Klein- Gordon Schrödinger (KGS) equations, Klein-Gordon Zakharov (KGZ) equations, Two dimensional Coupled Burgers’ equations and Two dimensional Reaction-Diffusion Brusselator equations. Different radial basis functions are used for this purpose. First order forward and second order central difference approximation is employed to the time derivative. The elementary stability and convergence of the proposed method are discussed. Accuracy of the method is assessed in terms of various error norms, number of nodal points and time step size. Performance of the proposed method is validated through examples from literature. Apart from ease of implementation, better accuracy is obtained. Comparison with existing methods such as finite difference methods, finite element methods, boundary element methods and spline methods is made to show the superiority and simple applicability of the mesh free method.