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Power Series Solutions of the One-Dimensional Flow Equation for Exponential and Linear Diffusivity Functions (Classic Reprint) - Couverture souple

Scott, Edward Joseph

 
9781527810389: Power Series Solutions of the One-Dimensional Flow Equation for Exponential and Linear Diffusivity Functions (Classic Reprint)

Synopsis

Power series methods for solving one-dimensional flow with exponential or linear diffusivity

This nonfiction guide presents a practical way to solve a diffusion‑type equation that models horizontal water movement in soils. It shows how a power series approach turns a complex boundary value problem into an initial‑value format you can compute, even when diffusivity varies with water content. The book also explains how to adapt the math to exponential and linear diffusivity functions and what that means for real soils.

Two clear sections frame the method and its use. Readers see the setup of the inflow and outflow problems, the role of dimensionless parameters, and how Taylor series provide approximate solutions. The text also discusses how to extend the range of validity with analytic continuation and how to implement the computations on a historic computer system, with results illustrated by graphs and example data from soil studies.
  • Learn the power series technique for different diffusivity models (exponential and linear).
  • Understand how boundary conditions shape solutions and the meaning of inflow versus outflow.
  • Follow a computational workflow: generate series coefficients, evaluate solutions, and extend convergence using analytic continuation.
  • Explore real-world applications with soil examples and interpretation of results.
Ideal for students, researchers, and professionals working with diffusion models in porous media, soil moisture movement, or related flow problems.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.