ہجر اثاثہ رہ جائے گا
درد خلاصہ رہ جائے گا
آدم زاد سے لغزش ہو گی
ہاتھ میں کاسہ رہ جائے گا
زخم تمھارے ہیرے موتی
درد ذرا سا رہ جائے گا
شعر نگر میں نام ہمارا
اچھا خاصا رہ جائے گا
سب کی پیاس بجھانے والا
دریا پیاسا رہ جائے گا
آج تمھارے ساتھ فضاؔ بس
جھوٹ دلاسا رہ جائے گا
Travelogue is a firm of literature which describes nation and people according to their history, civilization, politics, economics, and culture and presents cities and culture by showing the ideologies and manners/moralities, economics and society in the time when there were no transportation and the travelogues were the only source to get information. Because travelogue consists of the details about history and society, thus it has a tremendous amount of information and by offering characteristics of places and personalities. Moreover, travelogue describe personalities and events in the context of society and culture which provides a rich material to geologists, historicists as well as to the scholars of society ( sociologists) and students of literature and others.
Numerical Investigation of Convection Diffusion Reaction Systems This work is concerned with the numerical solution of selected convection-diffusion-reaction (CDR) type mathematical models with dominating convective and reactive terms, coupled with some algebraic equations. Five established CDR-type models are analyzed namely, the gas-solid reaction, chemotaxis, liquid chromatography, radiation hydrodynamical, and hy- perbolic heat condition models. These models are encountered in various scientific and engi- neering fields, such as chemical engineering, biological systems, astrophysics, heat transfer, and fluid dynamics. The Laplace transformation is applied as a basic tool to find the ana- lytical solutions of linear CDR models for different types of boundary conditions. However, for the nonlinear models, numerical techniques are the only tools to get physical solutions. The nonlinear transport and stiff source (reaction) terms of the governing differential equa- tions produce discontinuities and narrow peaks in the solution. It is difficult to capture steep variations in the solution through a less accurate numerical scheme. Therefore, ef- ficient and accurate numerical methods are needed to obtain physically reliable solutions in acceptable computational time. The objective of this thesis project is to develop and implement simpler, robust, and accurate numerical frameworks for the solution of one and two-dimensional CDR type systems. The space-time CE/SE-method, the discontinuous Galerkin (DG) finite element method , and different high resolution finite volume schemes (FVSs) are proposed to numerically approximate the solution of these models. Several case studies are carried out. The validity and performance of the suggested numerical techniques are revealed through test problems and by comparing their results with each other, analytical solutions, and the results of some available finite volume schemes in the literature.