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Fitted Numerical Methods for Singular Perturbation Problems: Error Estimates in the Maximum Norm for Linear Problems in One and Two Dimensions (Revise

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Fitted Numerical Methods for Singular Perturbation Problems: Error Estimates in the Maximum Norm for Linear Problems in One and Two Dimensions (Revise

4.85 46,292 ratings · 6,304 reviews
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Overview: Since the first edition of this book, the literature on fitted mesh methods for singularly perturbed problems has expanded significantly. Over the intervening years, fitted meshes have been shown to be effective for an extensive set of singularly perturbed partial differential equations. In the revised version of this book, the reader will find an introduction to the basic theory associated with fitted numerical methods for singularly perturbed differential equations. Fitted mesh methods focus on the appropriate distribution of the mesh points for singularly perturbed problems. The global errors in the numerical approximations are measured in the pointwise maximum norm. The fitted mesh algorithm is particularly simple to implement in practice, but the theory of why these numerical methods work is far from simple. This book can be used as an introductory text to the theory underpinning fitted mesh methods.Contents: Motivation for the Study of Singular Perturbation ProblemsSimple Examples of Singular Perturbation ProblemsNumerical Methods for Singular Perturbation ProblemsSimple Fitted Operator Methods in One DimensionSimple Fitted Mesh Methods in One DimensionConvergence of Fitted Mesh Difference Methods for Linear Reaction-Diffusion Problems in One DimensionProperties of Upwind Finite Difference Operators on Piecewise Uniform Fitted MeshesConvergence of Fitted Mesh Finite Difference Methods for Linear Convection-Diffusion Problems in One DimensionFitted Mesh Finite Element Methods for Linear Convection-Diffusion Problems in One DimensionConvergence of Schwarz Iterative Methods for Fitted Mesh Methods in One DimensionLinear Convection-Diffusion Problems in Two Dimensions and Their Numerical SolutionBounds on the Derivatives of Solutions of Linear Convection-Diffusion Problems in Two Dimensions with Regular Boundary LayersConvergence of Fitted Mesh Finite Difference Methods for Linear Convection-Diffusion Problems in Two Dimensions with Regular Boundary LayersLimitations of Fitted Operators Methods on Uniform Rectangular Meshes for Problems with Parabolic Boundary LayersFitted Numerical Methods for Problems with Initial and Parabolic Boundary LayersReadership: Scientists and engineers in applied mathematics and mathematical physics.

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Pages 191
Publisher World Scientific Publishing Company
Published January 1, 2012
ISBN 18651097
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G I Shishkin
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G I Shishkin writes contemporary fiction and has always been fascinated by character-driven stories. They hold a degree in English Literature and previously worked as an editor before transitioning to writing their own books. G I Shishkin lives with their spouse and a very vocal rescue cat.

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Honestly one of the most premium reading experiences lately. The author orchestrated a breathtaking finale. Truly a work of art. Worth every moment spent reading.
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I was completely blown away. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I am now a lifelong fan of this author.
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Such a rich narrative. The prose is exquisite. It’s accessible yet undeniably sophisticated. A true literary gem.
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Exceeded all my expectations. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I am now a lifelong fan of this author.
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I was completely blown away. The author orchestrated a breathtaking finale. Truly a work of art. An absolute must-read for connoisseurs of the genre.
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Honestly one of the most premium reading experiences lately. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An absolute must-read for connoisseurs of the genre.
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Masterpiece from start to finish. I adored how the story unfolded. It kept me captivated without sacrificing elegance. A true literary gem.
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Masterpiece from start to finish. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An effortless 5 stars.
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Such a rich narrative. The prose is exquisite. It’s accessible yet undeniably sophisticated. I am now a lifelong fan of this author.
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George Young
George Young July 11, 2024
I thoroughly enjoyed the elegance of it. The protagonist was compelling, though some subplots felt slightly overshadowed. Quite impressive overall.
Dorothy Williams
Dorothy Williams August 17, 2025
Masterpiece from start to finish. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An absolute must-read for connoisseurs of the genre.
Sarah Gonzalez
Sarah Gonzalez October 03, 2025
Honestly one of the most premium reading experiences lately. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I will undoubtedly revisit this masterpiece.
Donna Diaz
Donna Diaz January 08, 2024
A profoundly satisfying read. The prose is exquisite. It’s accessible yet undeniably sophisticated. An absolute must-read for connoisseurs of the genre.
George Lee
George Lee January 11, 2025
Took a moment to build, but the payoff was spectacular. The middle had a deliberate pace, but the climax was phenomenal. A very distinguished novel.
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