Hagag 2023a - Revision history

Ahmedshehata at 11:25, 5 March 2024

2024-03-05T11:25:20Z

Rimni: /* 4.2 Example 2 */

2024-02-20T11:54:59Z

‎4.2 Example 2

Rimni at 11:52, 20 February 2024

2024-02-20T11:52:48Z

Rimni at 11:49, 20 February 2024

2024-02-20T11:49:55Z

Rimni at 11:48, 20 February 2024

2024-02-20T11:48:51Z

Rimni: /* 4.1 Example 1 */

2024-02-20T11:47:32Z

‎4.1 Example 1

Rimni at 11:46, 20 February 2024

2024-02-20T11:46:36Z

Rimni at 11:44, 20 February 2024

2024-02-20T11:44:49Z

Rimni at 11:43, 20 February 2024

2024-02-20T11:43:53Z

Rimni at 11:42, 20 February 2024

2024-02-20T11:42:00Z

@@ Line 1,309: / Line 1,309: @@
 ==Acknowledgments==
-Princess Nourah bint Abdulrahman University Researchers Supporting Project number (PNURSP2024R215), Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia.
+Princess Nourah bint Abdulrahman University Researchers Supporting Project number (PNURSP2024R522), Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia.
 ==References==

@@ Line 1,046: / Line 1,046: @@
 | style="text-align: center;" | <math>\omega _{1}(\vartheta ,\iota )  =  \frac{45\kappa \iota ^{\sigma }\hbox{sech}^{2}(\kappa (\vartheta{-\eta}))}{6859\Gamma (\sigma{+1)}}\Bigl\{16\left(19\sqrt{209}\kappa \left(4\kappa ^{2}+1\right)-165\right)</math><math>\tanh (\kappa (\vartheta{-\eta}))-152\sqrt{209}\zeta +\hbox{ sech}^{2}(\kappa (\vartheta{-\eta}))</math>
 |-
-| style="text-align: center;" | <math>     \left(209\sqrt{209}\zeta{+\tanh}(\kappa (\vartheta{-\eta}))\left(165\left(152\sqrt{209}\kappa ^{3}-121\right)</math><math>\hbox{ sech}^{2}(\kappa (\vartheta{-\eta}))-76\sqrt{209}\kappa \left(224\kappa ^{2}+11\right)+18150\right)\right)\Bigr\}, </math>
+| style="text-align: center;" | <math>     \left(209\sqrt{209}\zeta{+\tanh}(\kappa (\vartheta{-\eta}))\left(165\left(152\sqrt{209}\kappa ^{3}-121\right)\hbox{ sech}^{2}(\kappa (\vartheta{-\eta}))-76\sqrt{209}\kappa \left(224\kappa ^{2}+11\right)+18150\right)\right)\Bigr\}, </math>
 |}
 | style="width: 5px;text-align: right;white-space: nowrap;" | (59)

@@ Line 1,044: / Line 1,044: @@
 {| style="text-align: left; margin:auto;width: 100%;"
 |-
-| style="text-align: center;" | <math>\omega _{1}(\vartheta ,\iota )  =  \frac{45\kappa \iota ^{\sigma }\hbox{sech}^{2}(\kappa (\vartheta{-\eta}))}{6859\Gamma (\sigma{+1)}}\Bigl\{16\left(19\sqrt{209}\kappa \left(4\kappa ^{2}+1\right)-165\right)\tanh (\kappa (\vartheta{-\eta}))-152\sqrt{209}\zeta +\hbox{ sech}^{2}(\kappa (\vartheta{-\eta}))</math>
+| style="text-align: center;" | <math>\omega _{1}(\vartheta ,\iota )  =  \frac{45\kappa \iota ^{\sigma }\hbox{sech}^{2}(\kappa (\vartheta{-\eta}))}{6859\Gamma (\sigma{+1)}}\Bigl\{16\left(19\sqrt{209}\kappa \left(4\kappa ^{2}+1\right)-165\right)</math><math>\tanh (\kappa (\vartheta{-\eta}))-152\sqrt{209}\zeta +\hbox{ sech}^{2}(\kappa (\vartheta{-\eta}))</math>
 |-
-| style="text-align: center;" | <math>     \left(209\sqrt{209}\zeta{+\tanh}(\kappa (\vartheta{-\eta}))\left(165\left(152\sqrt{209}\kappa ^{3}-121\right)\hbox{ sech}^{2}(\kappa (\vartheta{-\eta}))-76\sqrt{209}\kappa \left(224\kappa ^{2}+11\right)+18150\right)\right)\Bigr\}, </math>
+| style="text-align: center;" | <math>     \left(209\sqrt{209}\zeta{+\tanh}(\kappa (\vartheta{-\eta}))\left(165\left(152\sqrt{209}\kappa ^{3}-121\right)</math><math>\hbox{ sech}^{2}(\kappa (\vartheta{-\eta}))-76\sqrt{209}\kappa \left(224\kappa ^{2}+11\right)+18150\right)\right)\Bigr\}, </math>
 |}
 | style="width: 5px;text-align: right;white-space: nowrap;" | (59)

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 {| style="text-align: left; margin:auto;width: 100%;"
 |-
-| style="text-align: center;" | <math>\Upsilon \left(\omega (\vartheta ,\iota )\right)=D_{\iota }^{\sigma }\omega (\vartheta ,\iota )=\frac{\partial ^{\sigma }\omega (\vartheta ,\iota )}{\partial \iota ^{\sigma }},\quad \Phi \left(\omega (\vartheta ,\iota )\right)=</math><math> \omega (\vartheta ,\iota )\frac{\partial \omega (\vartheta ,\iota )}{\partial \vartheta }+\frac{\partial ^{2}\omega (\vartheta ,\iota )}{\partial \vartheta ^{2}}</math><math>+\frac{\partial ^{4}\omega (\vartheta ,\iota )}{\partial \vartheta ^{4}},\quad w(\vartheta ,\iota )=0. </math>
+| style="text-align: center;" | <math>\Upsilon \left(\omega (\vartheta ,\iota )\right)=D_{\iota }^{\sigma }\omega (\vartheta ,\iota )=\frac{\partial ^{\sigma }\omega (\vartheta ,\iota )}{\partial \iota ^{\sigma }},\quad</math><math> \Phi \left(\omega (\vartheta ,\iota )\right)= \omega (\vartheta ,\iota )\frac{\partial \omega (\vartheta ,\iota )}{\partial \vartheta }+\frac{\partial ^{2}\omega (\vartheta ,\iota )}{\partial \vartheta ^{2}}</math><math>+\frac{\partial ^{4}\omega (\vartheta ,\iota )}{\partial \vartheta ^{4}},\quad </math><math> w(\vartheta ,\iota )=0. </math>
 |}
 | style="width: 5px;text-align: right;white-space: nowrap;" | (42)

@@ Line 832: / Line 832: @@
 {| style="text-align: left; margin:auto;width: 100%;"
 |-
-| style="text-align: center;" | <math>\Upsilon \left(\omega (\vartheta ,\iota )\right)=D_{\iota }^{\sigma }\omega (\vartheta ,\iota )=\frac{\partial ^{\sigma }\omega (\vartheta ,\iota )}{\partial \iota ^{\sigma }},\quad \Phi \left(\omega (\vartheta ,\iota )\right)=\omega (\vartheta ,\iota )\frac{\partial \omega (\vartheta ,\iota )}{\partial \vartheta }+\frac{\partial ^{2}\omega (\vartheta ,\iota )}{\partial \vartheta ^{2}}+\frac{\partial ^{4}\omega (\vartheta ,\iota )}{\partial \vartheta ^{4}},\quad w(\vartheta ,\iota )=0. </math>
+| style="text-align: center;" | <math>\Upsilon \left(\omega (\vartheta ,\iota )\right)=D_{\iota }^{\sigma }\omega (\vartheta ,\iota )=\frac{\partial ^{\sigma }\omega (\vartheta ,\iota )}{\partial \iota ^{\sigma }},\quad \Phi \left(\omega (\vartheta ,\iota )\right)=</math><math> \omega (\vartheta ,\iota )\frac{\partial \omega (\vartheta ,\iota )}{\partial \vartheta }+\frac{\partial ^{2}\omega (\vartheta ,\iota )}{\partial \vartheta ^{2}}</math><math>+\frac{\partial ^{4}\omega (\vartheta ,\iota )}{\partial \vartheta ^{4}},\quad w(\vartheta ,\iota )=0. </math>
 |}
 | style="width: 5px;text-align: right;white-space: nowrap;" | (42)

← Older revision		Revision as of 11:47, 20 February 2024
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−	<div style="font-size: 75%;text-align:center;">'''Table 1'''. Compare numerical calculations of analytical solutions <math>\omega \left(\vartheta ,\iota \right)</math> of Eq. ([[#eq-19\|19]]) ~~<br>~~ obtained by TAM algorithm and NDM with exact, and q-HATM solutions at <math>\sigma=1</math>, <math>\kappa =\frac{1}{2\sqrt{19}}</math>, <math>\zeta=5</math> <math>,\eta=-25</math></div>	+	<div style="font-size: 75%;text-align:center;">'''Table 1'''. Compare numerical calculations of analytical solutions <math>\omega \left(\vartheta ,\iota \right)</math> of Eq. ([[#eq-19\|19]]) obtained by TAM algorithm and NDM with exact, <br> and q-HATM solutions at <math>\sigma=1</math>, <math>\kappa =\frac{1}{2\sqrt{19}}</math>, <math>\zeta=5</math> <math>,\eta=-25</math></div>

	<div id='tab-1'></div>		<div id='tab-1'></div>

← Older revision		Revision as of 11:46, 20 February 2024
Line 606:		Line 606:


−	<div style="font-size: 75%;text-align:center;">'''Table 1'''. Compare numerical calculations of analytical solutions <math>\omega \left(\vartheta ,\iota \right)</math> of Eq. ([[#eq-19\|19]]) obtained by TAM algorithm and NDM with exact, and q-HATM solutions at <math>\sigma=1</math>, <math>\kappa =\frac{1}{2\sqrt{19}}</math>, <math>\zeta=5</math> <math>,\eta=-25</math></div>	+	<div style="font-size: 75%;text-align:center;">'''Table 1'''. Compare numerical calculations of analytical solutions <math>\omega \left(\vartheta ,\iota \right)</math> of Eq. ([[#eq-19\|19]]) <br> obtained by TAM algorithm and NDM with exact, and q-HATM solutions at <math>\sigma=1</math>, <math>\kappa =\frac{1}{2\sqrt{19}}</math>, <math>\zeta=5</math> <math>,\eta=-25</math></div>

	<div id='tab-1'></div>		<div id='tab-1'></div>

← Older revision		Revision as of 11:44, 20 February 2024
Line 606:		Line 606:


−	<div style="font-size: 75~~%;width:55~~%;text-align:center;">'''Table 1'''. Compare numerical calculations of analytical solutions <math>\omega \left(\vartheta ,\iota \right)</math> of Eq. ([[#eq-19\|19]]) obtained by TAM algorithm and NDM with exact, and q-HATM solutions at <math>\sigma=1</math>, <math>\kappa =\frac{1}{2\sqrt{19}}</math>, <math>\zeta=5</math> <math>,\eta=-25</math></div>	+	<div style="font-size: 75%;text-align:center;">'''Table 1'''. Compare numerical calculations of analytical solutions <math>\omega \left(\vartheta ,\iota \right)</math> of Eq. ([[#eq-19\|19]]) obtained by TAM algorithm and NDM with exact, and q-HATM solutions at <math>\sigma=1</math>, <math>\kappa =\frac{1}{2\sqrt{19}}</math>, <math>\zeta=5</math> <math>,\eta=-25</math></div>

	<div id='tab-1'></div>		<div id='tab-1'></div>

← Older revision		Revision as of 11:43, 20 February 2024
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−	<div ~~class="center"~~ style="font-size: 75%;width:55%;text-align:center;">'''Table 1'''. Compare numerical calculations of analytical solutions <math>\omega \left(\vartheta ,\iota \right)</math> of Eq. ([[#eq-19\|19]]) obtained by TAM algorithm and NDM with exact, and q-HATM solutions at <math>\sigma=1</math>, <math>\kappa =\frac{1}{2\sqrt{19}}</math>, <math>\zeta=5</math> <math>,\eta=-25</math></div>	+	<div style="font-size: 75%;width:55%;text-align:center;">'''Table 1'''. Compare numerical calculations of analytical solutions <math>\omega \left(\vartheta ,\iota \right)</math> of Eq. ([[#eq-19\|19]]) obtained by TAM algorithm and NDM with exact, and q-HATM solutions at <math>\sigma=1</math>, <math>\kappa =\frac{1}{2\sqrt{19}}</math>, <math>\zeta=5</math> <math>,\eta=-25</math></div>

	<div id='tab-1'></div>		<div id='tab-1'></div>

← Older revision		Revision as of 11:42, 20 February 2024
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−	<div class="center" style="font-size: 75%;width:~~600px~~;text-align:center;">'''Table 1'''. Compare numerical calculations of analytical solutions <math>\omega \left(\vartheta ,\iota \right)</math> of Eq. ([[#eq-19\|19]]) obtained by TAM algorithm and NDM with exact, and q-HATM solutions at <math>\sigma=1</math>, <math>\kappa =\frac{1}{2\sqrt{19}}</math>, <math>\zeta=5</math> <math>,\eta=-25</math></div>	+	<div class="center" style="font-size: 75%;width:55%;text-align:center;">'''Table 1'''. Compare numerical calculations of analytical solutions <math>\omega \left(\vartheta ,\iota \right)</math> of Eq. ([[#eq-19\|19]]) obtained by TAM algorithm and NDM with exact, and q-HATM solutions at <math>\sigma=1</math>, <math>\kappa =\frac{1}{2\sqrt{19}}</math>, <math>\zeta=5</math> <math>,\eta=-25</math></div>

	<div id='tab-1'></div>		<div id='tab-1'></div>