The Principle of Superposition and Its Application In Ground-water Hydraulics

U.S. Geological Survey, Techniques of Water-Resources Investigations, Book 3, Chapter B6

By Thomas E. Reilly, O. Lehn Franke, and Gordon D. Bennett

Table of Contents

Preface

Abstract

Introduction

Purpose and Scope

Acknowledgment

Linear systems and linear equations

Definition of superposition

Application of superposition to a simple hydrologic system

Mathematical demonstration of superposition concept

Boundary conditions, stresses, and initial conditions in models that use superposition

Problem 1

Exercise

Discussion

Application of superposition in a well problem

Advantages of superposition

Constraints on the use of superposition

Problem 2

Exercise

Discussion

Application of superposition to nonlinear systems

Summary and concluding remarks

References cited

Appendixes:

1: Discussion of the solution of differential equations and the role of boundary conditions

2: Recognition of linear and nonlinear differential equations

3: Completed worksheets

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