Numerical Analysis for Science, Engineering and Technology

Numerical Solution for Partial Differential Equations

Author(s): Said Gamil Ahmed Sayed Ahmed, Hossein Jafari, Mukhtar Yagoub Youssif and Roberto Datja

Pp: 218-258 (41)

DOI: 10.2174/9781681086514118010007

* (Excluding Mailing and Handling)

Abstract

Partial differential equations have gained great interest due to their efficiency in describing the mathematical model of several physical phenomena and engineering applications. This chapter starts by a general definition for partial differential equations followed by some of the famous analytical methods of solutions and a brief description of major numerical methods for solving partial differential equations.


Keywords: Complex Fourier expansion, Definition of partial differential equation, Half-range expansion, Odd and even function, Types of partial differential equation.

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      • 13. app/Models/UserAccess/UserAccess.php:1266
      • 14. app/Http/Controllers/ChapterController.php:1518
      • 15. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 16. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
      • 17. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
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      640μsalphaeurekaselec_live_10_06_2022UserAccess.php#1266
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      • 13. app/Models/UserAccess/UserAccess.php:1266
      • 14. app/Http/Controllers/ChapterController.php:1549
      • 15. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 16. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
      • 17. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
    • select b.banner_link, b.banner_name, b.banner_script, b.banner_remarks, b.banner_file_name, b.banner_placement, bd.content_type, bd.content_id from `tbl_banner` as `b` inner join `tbl_banner_detail` as `bd` on `bd`.`banner_id` = `b`.`banner_id` inner join `users` as `u` on `u`.`id` = `b`.`updated_by` where `b`.`banner_ebook` = 1 and `bd`.`content_type` = 'B' and `bd`.`content_id` = 2447 and `b`.`banner_from_date` <= 1740550967 and `b`.`banner_to_date` >= 1740550967 and `b`.`banner_status` = 'A' order by `b`.`banner_id` desc
      1.08msalphaeurekaselec_live_10_06_2022Banner.php#95
      Bindings
      • 0: 1
      • 1: B
      • 2: 2447
      • 3: 1740550967
      • 4: 1740550967
      • 5: A
      Backtrace
      • 13. app/Models/Banner.php:95
      • 14. app/Http/helpers.php:404
      • 17. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
      • 18. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • 19. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:73
    • select count(*) as aggregate from `uc_cart_products` where cart_id='549a66695b8f2380b8ba51c552085c36'
      220μsalphaeurekaselec_live_10_06_2022Cart.php#271
      Backtrace
      • 15. app/Models/Cart.php:271
      • 16. view::layouts._header:260
      • 18. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
      • 19. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • 20. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:73
    App\Models\Keywords
    5Keywords.php#?
    App\Models\Chapter
    1Chapter.php#?
    App\Models\Ebook
    1Ebook.php#?
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        uc_cart_id
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        array:1 [ "url" => "https://alpha.eurekaselect.com/chapter/12108" ]
        _flash
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        PHPDEBUGBAR_STACK_DATA
        []
        path_info
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        status_code
        200
        
        status_text
        OK
        format
        html
        content_type
        text/html; charset=UTF-8
        request_query
        []
        
        request_request
        []
        
        request_headers
        0 of 0
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        request_cookies
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        array:1 [ "wayfindertarget" => null ]
        response_headers
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        ClearShow all
        Date ↕MethodURLData
        #12025-02-26 06:22:47GET/chapter/12108112187