8 (L{Lun(t)}) = 8 (sm L{un(t)} – sm-¹un (0) - ... -u (m-1) ( = s™ 8 (L{un(t)}). Therefore, we get (0)) L{λ(t)} sm Therefore, we have the following iteration algorithm: 1 (m). L{un+1(t)} = L{un(t)} - L{L(m³ un(t) + R un(t) + N un(t) − 9 ; g(t)} sm (m). - = L{un(t)}-{Lun(t)}- L{Run(t) + Nun(t) − g(t)} = L{un(t)} - - sm sm sm (sm L{un(t)}-sm-un (0) L{Run(t) + Nun(t) − g(t)} -um-1) (0)) · + (0) %/n 2 + (0) ³n == ամ 1 (m-1) + sm Un '(0) - 1 sm L{Run(t) + Nun(t) − g(t)} Finally, the approximate solution is given by u(x,t) = lim un(x,t) 12-00 to solve the following partial differential equations: E u₁+uuxuxx, u(x, 0) = x, 00 00

8 (L{Lun(t)}) = 8 (sm L{un(t)} – sm-¹un (0) - ... -u (m-1) ( = s™ 8 (L{un(t)}). Therefore, we get (0)) L{λ(t)} sm Therefore, we have the following iteration algorithm: 1 (m). L{un+1(t)} = L{un(t)} - L{L(m³ un(t) + R un(t) + N un(t) − 9 ; g(t)} sm (m). - = L{un(t)}-{Lun(t)}- L{Run(t) + Nun(t) − g(t)} = L{un(t)} - - sm sm sm (sm L{un(t)}-sm-un (0) L{Run(t) + Nun(t) − g(t)} -um-1) (0)) · + (0) %/n 2 + (0) ³n == ամ 1 (m-1) + sm Un '(0) - 1 sm L{Run(t) + Nun(t) − g(t)} Finally, the approximate solution is given by u(x,t) = lim un(x,t) 12-00 to solve the following partial differential equations: E u₁+uuxuxx, u(x, 0) = x, 00 00

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.2: Direct Methods For Solving Linear Systems

Problem 3CEXP

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