Inverse Differential Quadrature Method and its Application in Engineering

Authoritative reference introducing iDQM as a numerical tool to accurately perform high fidelity analyses efficiently for solving problems in engineering governed by higher-order ordinary and partial differential equations. Inverse Differential Quadrature Method and its Application in Engineering is the first book to comprehensively cover the development of a new numerical solution technique: the inverse differential quadrature method (iDQM), as an indirect approximation technique that can circumvent numerical differentiation-induced errors in the solution of systems of higher-order differential equations. The book's introduction highlights the historical development of numerical methods in the field while emphasising the significance of strong-form solution methods. Detailed derivations of iDQM formulations in one- and two-dimensions, approximation procedures, and error quantification are described. The subsequent chapters describe the application of iDQM to many fields of engineering including structures, heat flow, fluids, waves and multiphysics problems. Example applications covering linear and nonlinear systems are demonstrated with simple and detailed discretisation steps to aid reader understanding of iDQM. MATLAB codes for many of the illustrative examples in the book are provided to ease implementation and practice for readers. Written by a team of highly qualified academics, Inverse Differential Quadrature Method and its Application in Engineering discusses sample topics including: High fidelity linear and non-linear structural analyses of variable-stiffness curved beams, arbitrary-shaped plates, cylindrical and spherical shells governed by unified formulation kinematics. iDQM error formulation and its effect on spectral convergence. Accurate and efficient solutions of non-structural problems governed by, for example, Korteweg-de Vries (KdV) wave, Helmholtz, convection-diffusion and steady state heat conduction equations and nonlinear one- and two-dimensional scalar combustion models. Strategies to alleviate mathematical ill-conditioning of system matrices employing novel preconditioning techniques. Inverse Differential Quadrature Method and its Application in Engineering is an essential reference for researchers and engineers performing advanced numerical analysis across a range of applications in the mechanical, aerospace, chemical, and civil engineering industries, along with graduate students in related programs of study.