Tchebychev Polynomial Approximations for mthm^{th} Order Boundary Value Problems

Higher order boundary value problems (BVPs) play an important role modeling various scientific and engineering problems. In this article we develop an efficient numerical scheme for linear $m^{th}$ order BVPs. First we convert the higher order BVP to a first order BVP. Then we use Tchebychev orthogonal polynomials to approximate the solution of the BVP as a weighted sum of polynomials. We collocate at Tchebychev clustered grid points to generate a system of equations to approximate the weights for the polynomials. The excellency of the numerical scheme is illustrated through some examples.Comment: 21 pages, 10 figure

Fast and Efficient Numerical Methods for an Extended Black-Scholes Model

An efficient linear solver plays an important role while solving partial differential equations (PDEs) and partial integro-differential equations (PIDEs) type mathematical models. In most cases, the efficiency depends on the stability and accuracy of the numerical scheme considered. In this article we consider a PIDE that arises in option pricing theory (financial problems) as well as in various scientific modeling and deal with two different topics. In the first part of the article, we study several iterative techniques (preconditioned) for the PIDE model. A wavelet basis and a Fourier sine basis have been used to design various preconditioners to improve the convergence criteria of iterative solvers. We implement a multigrid (MG) iterative method. In fact, we approximate the problem using a finite difference scheme, then implement a few preconditioned Krylov subspace methods as well as a MG method to speed up the computation. Then, in the second part in this study, we analyze the stability and the accuracy of two different one step schemes to approximate the model.Comment: 29 pages; 10 figure

Spatiotemporal Orthogonal Polynomial Approximation for Partial Differential Equations

Starting with some fundamental concepts, in this article we present the essential aspects of spectral methods and their applications to the numerical solution of Partial Differential Equations (PDEs). We start by using Lagrange and Techbychef orthogonal polynomials for spatiotemporal approximation of PDEs as a weighted sum of polynomials. We use collocation at some clustered grid points to generate a system of equations to approximate the weights for the polynomials. We finish the study by demonstrating approximate solutions of some PDEs in one space dimension.Comment: 9 pages, 9 figure

Windowed Fourier Frames to Approximate Two-Point Boundary Value Problems

Boundary value problems arise while modeling various physical and engineering reality. In this communication we investigate windowed Fourier frames focusing two-point BVPs. We approximate BVPs using windowed Fourier frames. We present some numerical results to demonstrate the efficiency of such frame functions to approximate BVPs

Bait specificity in Hook and line fishery of River Ganga and associated conservation issues

Recent survey in lower 1,110 km stretch of River Ganga regarding ‘hook and line’ fishery revealed that fishers apply their inherited indigenous knowledge for selection of bait to harvest finfish and shellfish from river water. A total number of 26 different types of baits under 07 categories were recorded. Six varieties of fish species and four types of insects are found to be prevalent for catching carnivorous fishes. Five specially modified indigenous types of bait moulded with fish attractants were also documented. Bait-fish species association in hook and line fishery of river Ganga is discussed. Feeding habits of the target fishes was compared with the type of baits employed. Conservation issues associated with hook and line fishery is highlighted along with possible remedial measures. Different varieties of hook & line fishery which are in operation in river Ganga are briefly described. Indigenous Traditional Knowledge (ITK) associated with hook & line fishery needs to be properly documented and preserved for developing and encouraging ‘sport fishery’ in River Ganga

Bait specificity in Hook and line fishery of River Ganga and associated conservation issues

61-72Recent survey in lower 1,110 km stretch of River Ganga regarding ‘hook and line’ fishery revealed that fishers apply their inherited indigenous knowledge for selection of bait to harvest finfish and shellfish from river water. A total number of 26 different types of baits under 07 categories were recorded. Six varieties of fish species and four types of insects are found to be prevalent for catching carnivorous fishes. Five specially modified indigenous types of bait moulded with fish attractants were also documented. Bait-fish species association in hook and line fishery of river Ganga is discussed. Feeding habits of the target fishes was compared with the type of baits employed. Conservation issues associated with hook and line fishery is highlighted along with possible remedial measures. Different varieties of hook & line fishery which are in operation in river Ganga are briefly described. Indigenous Traditional Knowledge (ITK) associated with hook & line fishery needs to be properly documented and preserved for developing and encouraging ‘sport fishery’ in River Ganga

Numerical approximation of a nonlinear partial integro-differential equation

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