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Partial Differential Equations with Numerical Methods (Texts in Applied Mathematics)

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Partial Differential Equations with Numerical Methods (Texts in Applied Mathematics)

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    Available in PDF Format | Partial Differential Equations with Numerical Methods (Texts in Applied Mathematics).pdf | English
    Stig Larsson(Author) Vidar Thomee(Author)

The main theme is the integration of the theory of linear PDE and the theory of finite difference and finite element methods. For each type of PDE, elliptic, parabolic, and hyperbolic, the text contains onechapter on the mathematical theory of the differential equation, followed by one chapter on finite difference methods and one on finite element methods. The chapters on elliptic equations are preceded by a chapter on thetwo-point boundary value problem for ordinary differential equations. Similarly, the chapters on time-dependent problems are preceded by a chapter on the initial-value problem for ordinary differential equations. There is alsoone chapter on the elliptic eigenvalue problem and eigenfunction expansion. The presentation does not presume a deep knowledge of mathematical and functional analysis. The required background on linear functional analysis andSobolev spaces is reviewed in an appendix. The book is suitable for advanced undergraduate and beginning graduate students of applied mathematics and engineering.

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