t

x

$\alpha =0.2$

$\alpha =0.7$

$\alpha =1$

Exact Solution

Abs. error $\left|u_{Exact}-u_{LDM}\right|$

0.1

0.5

−0.84015035

−0.84719431

−0.84200369

−0.84170019

0.00030349875

1.0

−0.79140244

−0.83591408

−0.82723018

−0.82678633

0.00044385734

1.5

−0.74342766

−0.81235381

−0.8015035

−0.8010345

0.00046899813

2.0

−0.70107965

−0.77787419

−0.76618668

−0.76580255

0.00038413104

0.5

0.5

−0.81320446

−0.84990096

−0.84802561

−0.84516644

0.0028591668

1.0

−0.80726139

−0.84820141

−0.84379648

−0.84074121

0.0030552675

1.5

−0.7933088

−0.83324893

−0.82726913

−0.82471511

0.0025540116

2.0

−0.77275166

−0.8062717

−0.79944392

−0.79796266

0.001481259

0.9

0.5

−0.78865494

−0.83899061

−0.84577223

−0.83899395

0.0067782736

1.0

−0.78842909

−0.84297517

−0.85111767

−0.84525761

0.0058600603

1.5

−0.78148415

−0.83403147

−0.84330532

−0.83966942

0.003635898

2.0

−0.76844313

−0.81333057

−0.82306334

−0.82253964

0.00052370169