A fitted approximate method for solving singularly perturbed Volterra–Fredholm integro-differential equations with an integral boundary condition
Анотація
УДК 517.9
Підігнаний наближений метод розв'язування сингулярно збурених інтегро-диференціальних рівнянь Вольтерра–Фредгольма з інтегральною крайовою умовою
Розглянуто новий числовий підхід до розв'язування крайових задач для інтегро-диференціального рівняння Вольтерра–Фредгольма другого порядку з поведінкою шару та інтегральною граничною умовою. Запропоновано скінчен\-но-різницеву схему на відповідній сітці типу Шишкіна для отримання наближеного розв'язку поставленої задачі. Доведено, що запропонований метод є збіжним першого порядку за дискретною максимальною нормою. Наведено два числових приклади, що демонструють ефективність цього методу.
Посилання
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